RR LYRAE STARS IN LARGE MAGELLANIC CLOUD GLOBULAR CLUSTERS
By
Charles A. Kuehn III
A DISSERTATION
Submitted to Michigan State University in partial fulfillment of the requirements for the degree of
DOCTOR OF PHILOSOPHY
Astrophysics and Astronomy
2011 ABSTRACT
RR LYRAE STARS IN LARGE MAGELLANIC CLOUD GLOBULAR CLUSTERS
By
Charles A. Kuehn III
The Oosterhoff phenomenon presents a challenge to the accretion model for the buildup of at least part of the Milky Way halo. The existence of the Oosterhoff gap among the globular clusters in the halo of the Milky Way, while globular clusters in satellite galaxies tend to fall in this gap, seems to contradict the idea that the halo was formed through the accretion of objects similar to these current satellite galaxies. This dissertation seeks to better understand the Oosterhoff phenomenon through a systematic study of RR Lyrae stars in globular clusters in the Large Magellanic Cloud (LMC). Similar studies have been carried out on a set of Milky Way globular clusters which fall in the Oosterhoff-I (Oo-I) and Oosterhoff-II (Oo-II) classes but few studies with the requisite level of detail have been carried out on extragalactic objects. This dissertation set out to study the differences between RR Lyrae stars in Oo- I/II clusters and those in Oo-int clusters. Answers for three specific questions were sought. 1.) How do the properties of double-mode RR Lyrae stars in Oo-int clusters compare to those in Oo-I/II clusters? 2.) How do the positions of RR Lyrae stars on the Bailey diagram differ between stars in Oo-int clusters and those in Oo-I/II clusters. 3.) How do the physical properties of RR Lyrae stars, obtained through the Fourier decomposition of their light curves, change when going from Oo-I/II clusters to Oo-int clusters? The implications that this study has on the nature of the Oosterhoff dichotomy are also discussed. Copyright by CHARLES A. KUEHN III 2011 To Mom, Dad, Nana, Grandpa, and the rest of my family. To my grandmother and Papa who wished that they had been able to see me receive my PhD.
iv ACKNOWLEDGMENTS
There are many people who I wish to thank for their role in making this dissertation possible. First off I want to thank my adviser Horace Smith, whose guidance over the years not only made this dissertation possible, but allowed me to even get to this point in my career. M´arcio Catelan for his guidance over the years and his valuable comments on not only this thesis but other projects that we have collaborated on. Karen Kinemuchi for her proofreading of this dissertation and her advice on how to survive the dissertation writing and defense process. Nathan De Lee for his assis- tance on computer related matters when I was first starting out. The undergraduate students; Lisa Taylor, Randall McClellan, Kristina Looper, and Kyra Dame for their assistance with parts of this project. I wish to thank Catherine Kennedy for her support and friendship which were important in helping me get to this point. Thanks to Christopher Waters for the LATEX class used to format this thesis.
v TABLE OF CONTENTS
List of Tables...... viii
List of Figures...... x
List of Symbols...... xiii
1 Introduction...... 1
2 Milky Way Formation...... 4 2.1 StructureoftheMilkyWay ...... 4 2.2 FormationoftheMilkyWayHalo ...... 6
3 RR Lyrae Variables...... 10 3.1 Magnitudes...... 10 3.2 RR Lyrae Properties and Pulsation Mechanism ...... 12 3.3 RRLyraeClasses ...... 16 3.4 OosterhoffGroups ...... 18 3.5 OtherTypesofVariableStars...... 20
4 Observations, Data Reduction, and Physical Property Determina- tion...... 23 4.1 Observations and Image Processing ...... 23 4.2 Photometry and Variable Identification ...... 24 4.3 Determination of RR Lyrae Physical Properties ...... 26 4.3.1 FourierDecomposition...... 26 4.3.2 RRabVariables...... 27 4.3.3 RRcVariables ...... 29
5 NGC 1466...... 31 5.1 DataReductionforNGC1466 ...... 32 5.2 VariableStars ...... 34 5.2.1 RRLyraeStars...... 43 5.2.2 Comments on Individual RR Lyrae Stars ...... 44 5.2.3 RRdStars...... 45 5.2.4 OtherVariables...... 46 5.3 PhysicalPropertiesoftheRRLyraeStars ...... 50 5.4 DistanceModulus ...... 53 5.5 OosterhoffClassification...... 54
vi 6 Reticulum...... 59 6.1 VariableStars ...... 61 6.2 PhysicalPropertiesoftheRRLyraeStars ...... 69 6.3 DistanceModulus ...... 72 6.4 OosterhoffClassification...... 73
7 NGC 1786...... 75 7.1 VariableStars ...... 76 7.1.1 RRLyraeStars...... 83 7.2 PhysicalPropertiesoftheRRLyraeStars ...... 87 7.3 DistanceModulus ...... 91 7.4 OosterhoffClassification...... 92
8 NGC 2210...... 96 8.1 RRLyraeStars...... 97 8.2 PhysicalPropertiesoftheRRLyraeStars ...... 99 8.3 DistanceModulus ...... 101 8.4 OosterhoffClassification...... 101
9 Exploring Oosterhoff Intermediate Systems ...... 104 9.1 StructureoftheInstabilityStrip ...... 104 9.2 IndicatorsofOosterhoffStatus ...... 106 9.3 Bailey Diagrams for Oosterhoff Intermediate Objects ...... 110 9.3.1 NGC1466vsDraco ...... 113 9.3.2 NGC1466vsNGC2210...... 115 9.3.3 NGC2210vsNGC2257...... 116 9.3.4 NGC 1466 andNGC 2210 vs Oosterhoff I/IISystems . . . . 118 9.3.5 OosterhoffIntermediateLocus? ...... 120
10 Trends in Physical Properties ...... 122
11 Conclusions...... 136
A NGC 1466 Light Curves...... 141
B Reticulum Light Curves...... 178
C NGC 1786 Light Curves...... 198
References ...... 235
vii LIST OF TABLES
3.1 Filters and Their Wavelengths ...... 12
3.2 PropertiesofRRLyraestars...... 12
3.3 OosterhoffGroupProperties...... 18
4.1 InstrumentProperties...... 23
5.1 NGC 1466 Variables: Identification and Coordinates ...... 38
5.2 NGC 1466 Variables: Photometric Properties ...... 40
5.3 NGC1466Variables: Photometry ...... 43
5.4 NGC1466RRd’s: PhotometricParameters ...... 45
5.5 NGC1466RRabFourierCoefficients ...... 50
5.6 NGC1466RRcFourierCoefficients ...... 51
5.7 NGC1466RRabPhysicalProperties ...... 51
5.8 NGC1466RRcPhysicalProperties ...... 52
6.1 Reticulum Variables: Identification and Coordinates ...... 65
6.2 Reticulum Variables: Photometric Properties ...... 66
6.3 Reticulum RRd’s: Photometric Parameters ...... 67
6.4 Reticulum RRab Fourier Coefficients ...... 70
6.5 Reticulum RRc Fourier Coefficients ...... 70
6.6 Reticulum RRab Physical Properties ...... 71
6.7 Reticulum RRc Physical Properties ...... 72
7.1 NGC 1786 Variables: Identification and Coordinates ...... 77
viii 7.2 NGC 1786 Variables: Photometric Properties ...... 80
7.3 NGC1786RRd’s: PhotometricParameters ...... 83
7.4 NGC1786RRabFourierCoefficients ...... 89
7.5 NGC1786RRcFourierCoefficients ...... 89
7.6 NGC1786RRabPhysicalProperties ...... 90
7.7 NGC1786RRcPhysicalProperties ...... 90
8.1 NGC 2210 Variables: Photometric Properties ...... 97
8.2 NGC2210RRabFourierCoefficients ...... 99
8.3 NGC2210RRcFourierCoefficients ...... 99
8.4 NGC2210RRabPhysicalProperties ...... 100
8.5 NGC2210RRcPhysicalProperties ...... 100
9.1 PropertiesforStellarSystems ...... 112
10.1 RRab Physical Properties for Previously Studied Clusters ...... 122
10.2 RRc Physical Properties for Previously Studied Clusters ...... 123
10.3 RRab Physical Properties for LMC Clusters ...... 130
10.4 RRc Physical Properties for LMC Clusters ...... 130
ix LIST OF FIGURES
3.1 HRDiagramforRRLyraeStars ...... 14
3.2 RRLyraeBaileyClasses ...... 17
3.3 Average period vs metallicity for Globular Clusters ...... 19
3.4 Milky Way Halo Period-Amplitude Diagram ...... 21
4.1 ExampleofaFourierSeriesFit ...... 27
5.1 NGC1466CMD ...... 32
5.2 NGC1466CMD:HorizontalBranch ...... 33
5.3 NGC1466:RRabLightCurves ...... 35
5.4 NGC1466:RRcLightCurves ...... 36
5.5 NGC1466:RRdLightCurves...... 37
5.6 NGC1466PetersenDiagram ...... 47
5.7 NGC1466:ACLightCurve ...... 48
5.8 NGC 1466: B vs V Amplitudes ...... 49
5.9 NGC 1466: V -bandBaileyDiagram...... 55
5.10 NGC 1466: B-bandBaileyDiagram...... 56
5.11 NGC 1466: RRLyrae RawPeriod Distribution ...... 57
5.12 NGC 1466: RR Lyrae Fundamentalized Period Distribution ...... 58
6.1 ReticulumCMD ...... 60
6.2 ReticulumCMD:HorizontalBranch ...... 61
6.3 Reticulum: RRabLightCurves ...... 62
x 6.4 Reticulum:RRcLightCurves ...... 63
6.5 Reticulum:RRdLightCurves ...... 64
6.6 ReticulumPetersenDiagram...... 69
6.7 Reticulum: V -bandBaileyDiagram...... 73
6.8 Reticulum: B-bandBaileyDiagram...... 74
7.1 NGC1786CMD ...... 84
7.2 NGC1786CMD:HorizontalBranch ...... 85
7.3 NGC1786:RRabLightCurves ...... 86
7.4 NGC1786:RRcLightCurves ...... 87
7.5 NGC1786:RRdLightCurves...... 88
7.6 NGC 1786: V -bandBaileyDiagram...... 93
7.7 NGC 1786: B-bandBaileyDiagram...... 94
7.8 NGC1786PetersenDiagram ...... 95
8.1 NGC 2210: V -bandBaileyDiagram...... 102
8.2 NGC 2210: B-bandBaileyDiagram...... 103
9.1 InstabilityStripStructure ...... 105
9.2 hPabi vs Pab,min ...... 107
9.3 hPabi vs hPci ...... 108
9.4 hPabi vsNumberFractionofRRc’s ...... 109
9.5 hPabi vs Pc,max ...... 110
9.6 BaileyDiagramforCVnI ...... 111
9.7 NGC1466BaileyDiagram...... 112
9.8 NGC1466vsDraco: BaileyDiagram ...... 113
9.9 NGC1466vsDraco: PetersenDiagram...... 114
xi 9.10 NGC1466vsNGC2210: BaileyDiagram ...... 116
9.11 NGC2210vsNGC2257: BaileyDiagram ...... 117
9.12 NGC1466vsM3:BaileyDiagram ...... 118
9.13 NGC2210vsM15: BaileyDiagram...... 120
10.1 hTeff i vs Cluster Metallicity for RRc Stars in Previously Studied Globular Clusters ...... 125
10.2 hL/L⊙i vs Cluster Metallicity for RRc Stars in Previously Studied Glob- ularClusters...... 126
10.3 hM/M⊙i vs Cluster Metallicity for RRc Stars in Previously Studied Glob- ularClusters...... 127
10.4 hTeff i vs Cluster Metallicity for RRab Stars in Previously Studied Globular Clusters ...... 128
10.5 hMV i vs Cluster Metallicity for RRab Stars in Previously Studied Globular Clusters ...... 129
10.6 hTeff i vsClusterMetallicityforRRcStars ...... 131
10.7 hL/L⊙i vsClusterMetallicityforRRcStars ...... 132
10.8 hM/M⊙i vsClusterMetallicityforRRcStars ...... 133
10.9 hTeff i vsClusterMetallicityforRRabStars ...... 134
10.10hMV i vsClusterMetallicityforRRabStars ...... 135
A.1 Light curves for the variable stars in NGC 1466 ...... 141
B.1 Light curves for the variable stars in Reticulum ...... 178
C.1 Light curves for the variable stars in NGC 1786 ...... 198
xii LIST OF SYMBOLS
pc A parsec is 3.086 × 1016 meters...... 5
M⊙ MassoftheSun...... 12
R⊙ RadiusoftheSun...... 12
MV Absolute magnitude in the Johnson V filter...... 12
Teff Effectivetemperature...... 13
xiii Chapter 1: Introduction
One of the biggest unanswered questions in astronomy is: how did our galaxy, the Milky Way, form? Answering this question is important not only for understanding our place in the universe but the Milky Way also represents what is possibly our best laboratory for understanding how other large spiral galaxies form. While being located in the middle of the disk of the Galaxy presents us with some difficulties in terms of being able to get a full picture of the Galaxy, there is no other galaxy that we can observe in as much detail as the Milky Way. Current models of galaxy formation propose that large galaxies, like the Milky Way, form through the merging of smaller fragments. While this hierarchical forma- tion model has become commonly accepted, the nature of the smaller fragments that merged to form the Milky Way remains a mystery. In recent years the dwarf galaxies in the vicinity of the Milky Way have been looked at as being similar to the building blocks of the halo, the spherical distribution of stars that makes up the outer regions of the Milky Way. A large number of studies have been conducted attempting to determine if these dwarf galaxies resemble the objects that were accreted by the Milky Way to form the halo. Most of these studies have attempted to answer this question by comparing the content of elements heavier than helium in the dwarf galaxies to what is seen in the stars and globular clusters in the Galactic halo. These studies based on metallicity have yielded mixed results.
1 RR Lyrae stars represent another tool that can be used to study the formation of the Galactic halo. RR Lyrae are pulsating variable stars with periods on the order of a day or less. They are luminous stars which make them easy to observe. Studies of RR Lyrae stars in Milky Way globular clusters have shown that these clusters can be divided into two groups, called Oosterhoff groups, based on the properties of their RR Lyrae stars (Oosterhoff groups and other terms will be properly defined in subsequent chapters). These Oosterhoff groups are separated by a zone of avoidance called the Oosterhoff gap. When one looks at the RR Lyrae stars in the nearby dwarf galaxies and their globular clusters, the Oosterhoff gap is not present as these extragalactic objects fall in the gap, as well as in the two Oosterhoff groups. In fact these extragalactic systems seem to preferentially fall in the gap. The existence of these Oosterhoff intermediate (Oo-int) objects in the nearby dwarf galaxies and their absence in the Milky Way present a challenge to the hierarchical accretion model for Milky Way halo formation. If the halo formed through the accretion of objects similar to the present day dwarf galaxies, we would expect to see globular clusters in the halo with the same properties as in the dwarf galaxies. In order to fully understand how the Milky Way halo formed, we need to better understand the nature of Oo-int objects. This dissertation seeks to better understand this Oosterhoff phenomenon through a systematic study of globular clusters in the Large Magellanic Cloud (LMC). Similar studies have been carried out on Oosterhoff I (Oo-I) and Oosterhoff II (Oo-II) clusters in the Milky Way but very few extragalactic systems have been looked at with this level of detail. The observations carried out as part of this dissertation allow for a detailed comparison between these LMC clusters and those in the Milky Way. The primary goal of this dissertation is to better understand the nature of Oo-int objects. Answers to three specific questions are sought. 1.) How do the properties of double-mode RR Lyrae stars in Oo-int clusters compare to those in Oo-I/II clusters? 2.) How do the positions of RR Lyrae stars on the Bailey diagram differ between stars
2 in Oo-int clusters and those in Oo-I/II clusters. 3.) How do the physical properties of RR Lyrae stars, obtained through the Fourier decomposition of their light curves, change when going from Oo-I/II clusters to Oo-int clusters? The following chapters will discuss the previous work on this subject, the observations that were made and their results, and finally compare the observed clusters to previously studied globular clusters and dwarf galaxies.
3 Chapter 2: Milky Way Formation
This chapter presents a quick overview of the current understanding of the physical processes involved in the formation of the Milky Way and other large galaxies. This is meant to familiarize the reader with the topics that will be talked about later in this dissertation and thus particular attention is paid to the formation of the halo. This chapter is not meant as a thorough treatment of the subject; such a treatment is beyond the scope of this dissertation, but is discussed in Lee et al. (2011), Babusiaux et al. (2010) and the references contained within this chapter.
2.1 Structure of the Milky Way
The Milky Way is a barred-spiral galaxy that consists of three main parts: the central bulge, the flattened disk, and a dual halo. These components differ in terms of their gas and stellar content, dynamical motion, and formation history. The bulge is a tri-axial bar-shaped structure located at the center of the Milky Way. Most of the stars in the bulge are old, 10 − 12 Gyr, and display a wide range in metallicities, −1.5 ≤ [Fe/H] ≤ 0.75 (Zoccali, 2010). Metallicity is the astronomical term used to refer to the amount of elements heavier than helium in a star or other astronomical object. Typically iron is used as a proxy for the total content of the heavier elements, and the metallicity is expressed using the shorthand [Fe/H] which
4 relates the iron to hydrogen ratio in a star to the ratio in the Sun via the equation:
[Fe/H] = log(NFe/NH)star − log(NFe/NH)Sun (2.1)
where NFe and NH are the number density of iron and hydrogen atoms, respectively. When most people think of the Milky Way, they think of the spiral arms that are prominent in the commonly seen images of the Galaxy. These spiral arms are part of the disk of the Milky Way, a relatively thin component of the Galaxy that consists of stars, gas, and dust orbiting around the Galactic center in roughly circular orbits. The disk can be thought of as being made of two components, the thin and thick disks, named so due to their relative heights. The thin disk has a scale height of approximately 300pc and features a large amount of young stars due to ongoing star formation. Stars in the thin disk are relatively metal-rich, [Fe/H] ≥ −0.5, with younger stars being more metal-rich than older stars. The thick disk has a scale height of approximately 1 kpc and contains stars that are older and more metal-poor than the stars in the thin disk (Ostlie & Carroll, 1996; Lee et al., 2011). The final component of the Milky Way galaxy is the dual halo, a roughly spherical distribution of stars that surrounds the rest of the Galaxy. The stars in the halo tend to be some of the oldest and most metal-poor stars in the Galaxy. Like the disk, the halo is thought to consist of two components, the inner and outer halo. The inner halo is thought to be non-rotating, more flattened, and has a peak metallicity of [Fe/H] ≈ −1.6. In contrast, the outer halo is thought have a retrograde rotation, is roughly spherical, and contains stars that are generally more metal-poor than the inner halo, with a peak metallicity of [Fe/H] ≈ −2.2 (Carollo et al. 2011 and references therein). The halo also contains approximately 100 globular clusters, objects with 106 or more stars that all form at the same time from a giant collapsing gas cloud and that are gravitationally bound together. How the halo formed is one of the great open questions in astronomy and answering that question is crucial to constraining overall
5 formation models for the Milky Way as well as other barred spiral galaxies.
2.2 Formation of the Milky Way Halo
Early theories of Milky Way formation suggested that the Galaxy formed from a large cloud of gas that collapsed as it cooled, forming stars and globular clusters in the process (Eggen et al., 1962). This model predicted the existence of a metallicity gradient, where stars and clusters with higher metallicity occur at smaller galactic radii. This occurs because higher metallicity stars can only form at later times, after a previous generation of more metal-poor stars have had time to form and cast off heavier elements. In addition to being located at smaller galactic radii, higher metallicity stars are expected to have less eccentric orbits, as they form after the gas cloud has spun up in order to conserve angular momentum. Later observations did not find the expected trends between metallicity and galactic radii or orbital eccentricity, instead suggesting that the sample of stars used by Eggen et al. (1962) may have suffered from a selection bias (Chiba & Beers, 2000). While this model explains the formation of some parts of the Milky Way, such as the disk, it has been abandoned as an explanation for the origin of the halo; this is not say that the cloud collapse model has been abadoned entirely as there is evidence that it may be the method by which massive early-type galaxies form (Eliche-Moral et al., 2010). An alternate explanation for the formation of the Milky Way was devised by Searle & Zinn (1978), hereafter referred to as SZ. Instead of having the Galaxy form from the collapse of a single gas cloud, the SZ model had the inner region of the Galaxy form from the collapse of a large gas cloud while the halo of the Galaxy was formed by the accretion of smaller gas clouds. Stars and globular clusters would form in these smaller clouds and then mix with the contents of the Galaxy, forming the outer halo. The 1990s saw the development of the lambda-cold-dark-matter (ΛCDM) cos- mological model which predicted that large galaxies formed through the hierarchical
6 assembly of smaller subgalactic fragments. In this model, stars first form from gas in dark matter halos that are smaller than galaxies and over time these halos slowly merge together and grow in size (Bekki & Chiba, 2001), eventually reaching the size of the large spiral galaxies that we see today. When applied to the Milky Way halo, the ΛCDM model predicts that the halo was formed through the accretion of smaller galaxies (Bullock & Johnston, 2005; Abadi et al., 2006; Font et al., 2006). The contents of these smaller galaxies (their stars, gas, dust, globular clusters, and dark matter) merge with the Milky Way. The accretion process dissipates the smaller galaxies, spreading their contents around the halo of the Milky Way and over time making them indistinguishable from the remnants of previous mergers, as well as any pieces that may have formed within the Milky Way itself (Pe˜narrubia et al., 2005). Globular clusters in the smaller galaxies are dense enough that they are likely to survive the accretion process intact. If the Milky Way halo formed through this ΛCDM merger scenario, the next question to consider is: what did the building blocks of the halo look like? The Milky Way is not an isolated galaxy, instead it belongs to a group of galaxies known as the Local Group. The Local Group consists of two large spiral galaxies, the Milky Way and the Andromeda galaxy (M31), and dozens of dwarf galaxies. The building blocks of the halo may have resembled these present day dwarf satellite galaxies (Searle & Zinn, 1978; Zinn, 1993; Mackey & van den Bergh, 2005). Recent observations have yielded a great deal of data supporting not only the hierarchical merger model for halo formation but also suggesting that the smaller galaxies that were accreted during this process resemble the present day dwarf satellite galaxies of the Milky Way. One of the most crucial pieces of evidence in support of the merger model is the discovery of stellar streams in the halo. The first of these, the Sagittarius stream, was discovered by Ibata et al. (1994) and many others have been found since (Newberg et al., 2002; Belokurov et al., 2006, 2007). These stellar
7 streams originate from dwarf galaxies that are being tidally disrupted by the Milky Way. Forbes & Bridges (2010) recently carried out a study looking at the age-metallicity relationship of 93 Milky Way halo globular clusters for which deep color-magnitude diagrams could be obtained in the literature. They found that 27-47 of the globular clusters in their sample displayed an age-metallicity relationship that is similar to what is seen in the present day dwarf galaxies, suggesting that these clusters likely originated in dwarf galaxies and were later accreted into the Milky Way. In addition to looking at the overall trend of metallicity in stars in the Milky Way and nearby dwarf galaxies, the chemical abundance patterns in the stars of the Milky Way and nearby dwarf galaxies have been compared with mixed results. Pritzl et al. (2005b) compared previously published abundances of stars in the Galactic halo and dwarf galaxies and concluded that, based on the differences seen in the elemental abundance patterns, stars and globular clusters in the Milky Way halo could not have originated in the nearby dwarf galaxies. More recently, Frebel, Kirby, & Simon (2010) found that the Sculptor dwarf galaxy contains a star that displays the same elemental abundance pattern that is seen in metal-poor stars in the Milky Way halo. This star is extremally metal-poor, [Fe/H]= −3.8, and its discovery suggests that at least one dwarf galaxy can form the type of stars that make up the extremally metal-poor component of the Milky Way halo. Mucciarelli et al. (2010) recently carried out high- resolution spectrographic studies of red giant stars in three globular clusters in the LMC, finding that these clusters had elemental abundance patterns consistent with Milky Way globular clusters. Additional observations of stars in the nearby dwarf galaxies will be needed to ultimately resolve the issue of whether or not any of the dwarf spheroidals produce stars like the ones that make up the normal metal-poor population of the haloes. RR Lyrae stars represent an additional tool that can be used to investigate the
8 Galactic halo and its formation. RR Lyrae are relatively bright and can be found in all Galactic components as well as in globular clusters and nearby dwarf galaxies. These stars are some of the oldest stars in the Galaxy and existed at the time that the Galaxy was forming. RR Lyrae are relatively easy to identify in photometric time- series data sets and can also be used to establish distances. In Chapter 3 I discuss in more detail the stellar characteristics of RR Lyrae stars and how they can be utilized in the understanding of Milky Way halo formation.
9 Chapter 3: RR Lyrae Variables
RR Lyrae (RRL) stars are pulsating variable stars with periods that range from several hours to just over a day. RR Lyrae have been known since the late nineteenth century thanks to the work of E.C. Pickering and Solon Bailey (Pickering & Bailey, 1895). RR Lyrae stars are very useful in several different areas of astronomy. RRL have a very narrow range of luminosities and thus are excellent standard candles that can be used to determine distances within the Milky Way and to nearby galaxies. Studies of their pulsational characteristics are useful when attempting to understand stellar evolution as they provide information about the internal structure of the star. Additionally, pulsation theory can be used to determine the masses of RR Lyrae stars that pulsate in multiple modes; these masses can then be compared against those predicted by stellar evolution theory. As will be discussed in this dissertation, comparing the properties of RR Lyraes in the Milky Way and nearby dwarf galaxies places constraints on the merger model for Milky Way halo formation.
3.1 Magnitudes
Before the RR Lyrae stars are discussed in more detail, it is necessary to make a brief detour to discuss the magnitude system used by astronomers. Astronomers typically express the brightness of stars using a system of magnitudes that dates back to the ancient Greeks. The system was originally created by Greek astronomer Hipparchus as a means to rank how bright stars appeared; the brightest stars were first magnitude,
10 slightly dimmer stars were second magnitude and so forth. These magnitudes were originilly defined by the sensitivity of the human eye. Later, the magnitude system was quantified such that the difference in magnitudes between two objects is given by the equation, f1 m1 − m2 = −2.5log , (3.1) f2
where m1 and m2 are the magnitudes of the two objects and f1 and f2 are the fluxes received from those objects, respectively. As this equation clearly demonstrates, brighter objects have smaller magnitudes. For example, looking at two stars, Vega (magnitude≈ 0) and Spica (magnitude≈ 1), the flux received from Vega is 2.5 times the flux received from Spica. There are two types of magnitudes, apparent and absolute, which can be used to describe an object. Absolute magnitudes are based on the flux that would be received from an object if it were at a distance of 10 parsecs. As such, absolute magnitudes reflect the actual amount of light emitted by an object. Apparent magnitudes are based on the flux from an object that is received by an observer and thus are based not only on the luminosity of the object but also the distance to that object. If one knows both the absolute and apparent magnitude of an object, the distance to it can be calculated using the following equation:
M = m − 5 log(d)+5, (3.2) where M is the absolute magnitude of a source, m is the apparent magnitude, and d is the distance to the source measured in parsecs. The brightness of an object is typically measured in specific wavelength ranges which are created by using filters when taking observations. The three filters used in the observations for this dissertation are the Johnson-V , Johnson-B and the Cousins- I filters; the wavelength coverage of these filters, central wavelength and the width
11 at half maximum transmission, is summarized in Table 3.1. These filters were chosen as they have historically been the ones most used in studies of RR Lyrae stars.
Table 3.1: Filters and Their Wavelength Ranges
Filter Central Wavelength (Angstroms) FWHM (Angstroms)
B 4326 1269 V 5332 1073
I 8050 1500
3.2 RR Lyrae Properties and Pulsation Mecha- nism
RR Lyrae are old, Population II stars that were originally discovered in globular clusters with ages 10 billion years or more. RR Lyrae stars lie on the horizontal branch, meaning that they are fusing helium in their cores, where the horizontal branch crosses through the instability strip, Figure 3.1. RR Lyrae tend to be relatively metal poor, 0.0 ≤ [Fe/H] ≤ −2.5. Additional properties of RR Lyrae stars are summarized in Table 3.2.
Table 3.2: Properties of RR Lyrae Stars (Smith, 1995)
Property Value
[Fe/H] -2.5 to 0.0
Teff 6100 K to 7400 K
Mass ≈ 0.7 M⊙
Radius 4 to 6 R⊙
MV +0.6 ± 0.2 mag
12 Table 3.2: Properties of RR Lyrae stars. (continued)
Property Value
Period 0.2 to 1.2 days
Amplitude 0.2 to 2.0 mag in V Spectral Type A through F
Table 3.2 lists the absolute magnitude in the V -band for RR Lyrae stars as MV = +0.6 ± 0.2, however this is an average as there is a trend between absolute magnitude and the metallicity of the star, with metal-poor RR Lyraes being more luminous than metal-rich ones. Catelan & Cort´es (2008) used theoretical models fit to the star RR Lyrae itself to find that the absolute magnitude of an RR Lyrae star is
hMV i = (0.23 ± 0.04)[Fe/H]ZW 84 + (0.984 ± 0.127) (3.3)
where the metallicity of the star is given using the scale of Zinn & West (1984), hereafter referred to as ZW84. RR Lyrae stars vary due to the fact that they are intrinsically radially pulsating stars, the change in brightness in the V -passband occurring mainly due to the change
in effective temperature (Teff ) that occurs during the expansion and contraction of the star. The pulsations of an RR Lyrae can be described using the pulsation equation derived by Ritter (1879) which shows the relationship between the pulsational period and the density of the star,
Q = P ρ/ρ⊙, (3.4) p
where P is the pulsation period measured in days, ρ is the density of the star, ρ⊙ is the density of the Sun, and Q is the pulsation constant which is approximately 0.04 days for RR Lyrae stars that pulsate in the fundamental mode (Smith, 1995).
13 Figure 3.1: HR diagram for a typical globular cluster showing the brightness, MV , versus color, (B − V )0, for the stars in the cluster. Color is an indication of temper- ature with bluer stars being hotter and located toward the left on the diagram. The position of RRL stars on the horizontal branch, in the instability strip, is indicated. Figure from Smith (1995).
The radial pulsations of RR Lyrae stars are driven by the opacity of the outer layers of the stars which serves as a heat valve. The opacity of a region in a star is given by a Kramer’s law-like opacity,
n −s κ = κ0ρ T , (3.5)
where κ is the opacity, κ0 is a constant dependent on the composition of the stellar material, ρ is the density of the region, and T is the temperature of the region. For envelopes of stars where no abundant element is being ionized, n ≈ 1 and s ≈ 3.5.
14 This means that when the temperature increases, the opacity drops, allowing addi- tional radiation to escape and thus not driving a pulsation. However, if the envelope of the star contains an abundant element that is being ionized, s can become very small or negative. Thus an increase in temperature increases the opacity, trapping more radiation. This causes the outer layers of the star to expand until the drop in the density of the gas due to expansion is enough to lower the opacity to the point where radiation can once again escape. At this point the outer layers contract, increasing the density and temperature, resulting in an increase in opacity and causing the cycle to restart. Christy (1966) showed that the zone where helium is being doubly ionized is the most important in driving pulsations in RR Lyrae stars. The location of the zone where gas is being ionized in the star determines whether or not the star will pulsate with the κ-mechanism. The location of these partial ionization zones is largely dependent on the temperature of the star. If a star is too hot, its ionization zone is located near its surface where there is not enough material left to drive pulsations. Stars that are too cool suffer from an effect where the energy transport mechanism in their outer envelope is convective rather than radiative, damping the κ-mechanism. These temperatures set the location of the two edges of the instability strip seen in Figure 3.1. A second mechanism also involving the ionization zones in a star, may play a role in the pulsations of RR Lyrae stars. This mechanism, referred to as the γ-mechanism, is based on the fact that in ionization zones, energy that would normally go into raising the temperature of the gas can instead go into ionizing more of the gas. This means that the gas can absorb heat during compression, leading to a pressure maximum that occurs just after the star has fully contracted, which can drive pulsations (King & Cox, 1968).
15 3.3 RR Lyrae Classes
RR Lyrae stars can be divided into classes based on their pulsation mode and the shape of their light curves. Bailey & Pickering (1902) used light curve shape to classify RR Lyrae stars as “a”, “b”, or “c” type. Later the “a” and “b” classes were combined into one class, “ab”. RR Lyrae stars of type “ab” (RRab) are fundamental mode pulsators which fea- ture light curves that show a rapid increase in brightness followed by a slower decrease (Fig. 3.2). RRab stars tend to have periods between 0.4 and 1.2 days and amplitudes of 0.5 to 2.0 magnitudes in the V -band. RR Lyrae stars of type “c” (RRc) pulsate in the first overtone and feature more sinusoidal light curves (Fig. 3.2). RRc stars have shorter periods, P ≤ 0.4 days, and smaller amplitudes, ≤ 0.8 magnitudes in V , than their fundamental mode counter- parts. A class of RR Lyrae which pulsate in both the fundamental mode and the first overtone (RRd) were discovered by Jerzykiewicz & Wenzel (1977). The first overtone is the dominant mode in most RRd stars and thus their light curves are similar to RRc stars but with more scatter due the presence of the fundamental mode (Fig. 3.2). The ratio of the two pulsation periods in RRd stars can be used to determine masses for these stars (Petersen, 1973). Some RR Lyrae stars have been found to experience a periodic modulation of the light curve shape that occurs on time scales longer than that of the primary period. Despite being known for over a century (Blazhko , 1907), the cause of this Blazhko effect has yet to be determined.
16 Figure 3.2: Sample light curves for RRab, RRc, and RRd stars from Kuehn et al. (2011). The RRd light curve is plotted with the first overtone mode period. The magnitudes shown in the figure are included for the purpose of demonstrating the difference in amplitudes between the different classes.
17 3.4 Oosterhoff Groups
Oosterhoff (1939) noticed that globular clusters in the Milky Way could be divided into two groups based on the average periods and number fraction of their RR Lyrae stars. Though his original sample size was only five clusters, additional analysis (Oosterhoff, 1944; Sawyer, 1944) confirmed that this division existed and these groups were subsequently named after Oosterhoff. Oosterhoff I (Oo-I) clusters tend to have shorter average periods for their RR Lyraes, and are more metal-rich than Oosterhoff II (Oo-II) clusters (Smith, 1995). Oo-I clusters also tend to have fewer RRc stars
when compared to the total number of RR Lyrae stars in the cluster, nRRc/nRRL . Table 3.3 summarizes the properties of the Oo-I and Oo-II objects.
Table 3.3: Properties of the Oosterhoff Groups (Smith, 1995)
Property Oo-I Oo-II
hPabi 0.55 days 0.64 days
hPci 0.32 days 0.37 days
nRRc/nRRL 0.17 0.44 [Fe/H] > −1.7 < −1.7
A plot of the average RRab period (hPabi) vs cluster metallicity for Galactic globular clusters (Figure 3.3, left panel) clearly shows the two Oosterhoff groups as well as a zone of avoidance between them, the Oosterhoff gap. The right panel of
Figure 3.3 shows hPabi vs [Fe/H] for stellar systems in nearby dwarf galaxies. When one looks at the nearby dwarfs there is no Oosterhoff gap as the stellar systems in these dwarfs fall in the gap, as well as in the Oo-I and Oo-II groups. In fact, these extragalactic objects seem to preferentially lie in the gap (Catelan, 2009b). These Oosterhoff intermediate (Oo-int) objects, as the objects that fall into the gap are referred to, present a challenge to the accretion model for the formation of
18 Figure 3.3: Average period for RRab stars hPabi vs [Fe/H] for globular clusters in the Milky Way (left) and nearby dwarf galaxies and their globular clusters (right). Figure reprinted from Catelan (2009b) with permission. the Milky Way halo. Of the 43 Milky Way globular clusters that contain at least five identified RR Lyrae stars, only four of these clusters can be classified as Oo- int, and they are on the edge of the Oosterhoff gap. Looking at the nearby dwarf galaxies and their globular clusters, of the 36 objects with at least five identified RR Lyrae stars, 17 of them are classified as Oo-int. Performing a Kolmogorov-Smirnov test reveals that there is only a 1.8% chance that these two sets of objects are from the same parent population. If the Milky Way halo formed by accreting objects like the current dwarf galaxies, then we would expect to see RR Lyrae stars in the halo with the same Oosterhoff classification as we see in the dwarfs. The presence of the Oosterhoff gap when looking at the globular clusters in the Milky Way halo indicates that if the halo formed from accreting dwarf galaxies, these accreted galaxies did not look like our current dwarfs (Catelan, 2009a). One possible explanation for this Oosterhoff phenomenon could be that Oo-int dwarf galaxies have been accreted in the past but were completely disrupted during
19 the accretion process, leaving behind no globular clusters but instead disbursing all of their RR Lyrae stars into the field population of the halo. This possibility can be explored by looking at the Oosterhoff classification of the individual RR Lyrae stars in the field population of the halo. The Oosterhoff classification of an individual star can be determined by studying its location on a plot of period-vs-amplitude, called a Bailey diagram; this is most effective when looking at RRab stars. Figure 3.4 shows the period-amplitude diagram for RR Lyrae stars in the Milky Way halo obtained from data in the Sloan Digital Sky Survey (De Lee, 2008). Also plotted are the loci for RRab stars of Oo-I and Oo-II types. The majority of RRab stars are Oosterhoff I stars and, while there are some Oo-intermediate stars in the halo, there are not enough Oo-int stars to be consistent with the distribution of Oosterhoff types among the nearby dwarf galaxies and their globular clusters. Similar work done by Miceli et al. (2008) and Szczygiel et al. (2009) confirm the existence of the Oosterhoff dichotomy in the field stars of the Milky Way, both in the halo and in the region near the Sun. As was seen in the work by De Lee, Miceli et al., and Szcyzugiel et al., there are some Oo-int stars in the field but not enough of these stars to be consistent with the number of Oo-int objects in the nearby dwarf galaxies. If the hierarchical merger model for the formation of the Milky Way halo is true, the absence of Oo-int objects in the Milky Way needs to be explained. In this disser- tation I undertake a systematic survey of a group of globular clusters in the LMC with the goal of better understanding Oo-int objects and the differences between them and Oo-I/II objects.
3.5 Other Types of Variable Stars
While the primary goal of this dissertation was to study the RR Lyrae stars in the target globular clusters, variable stars of several other types were found in the process. This section is meant as a brief guide to these other types of variable stars.
20 2 2 RRab RRab RRc RRc OOI OOI OOII OOII 1.5 1.5
A 1 1
0.5 0.5
0 0 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 Log(P) Log(P)
Figure 3.4: Period-amplitude diagrams for RR Lyrae in the Milky Way halo from the Sloan Digital Sky Survey. The left panel shows the Oo-I and Oo-II lines from Clement & Rowe (2000). The right panel shows the Oo-I and Oo-II lines from Cacciari et al. (2005). Each of these lines were transformed into the g band by using Ag/AV =1.17. Figure from De Lee (2008). For interpretation of the references to color in this and all other figures, the reader is referred to the electronic version of this dissertation.
-Cepheids are pulsating supergiant stars that are located in the instability strip and which have periods in the range of 1 − 100 days. Cepheids can be divided into two classes: classical Cepheids and Type II Cepheids. -Classical Cepheids are younger stars, more massive than the Sun, which are crossing the instability strip in the later stages of their evolutionary lives. Classical Cepheids typically have pulsational amplitudes between 0.5 and 1.0 magnitude in V . They are span a wide range of luminosities, having absolute V magnitudes in the range of −6.0 ≤ MV ≤ −0.5. -Type II Cepheids are older stars that are less massive than the Sun, 0.5 − 0.6 solar masses. Type II Cepheids have similar amplitudes to their classical Cepheid counterparts but are typically less luminous, having absolute magnitudes of −3 ≤
MV ≤ 0.
21 -Anomalous Cepheids (AC) are another class of pulsating giant star that is located within the instability strip. ACs typically have masses between 1 and 1.5 solar masses and are either young stars, ≈ 5 Gyr old, or older stars that have gained mass from being in a binary (Pritzl et al., 2002). AC stars have periods between 0.4 and 1.6 days and absolute V magnitudes of −1.4 ≤ MV ≤ 0.4. -Delta Scuti (DS) stars are pulsating main sequence stars, meaning that they are still fusing hydrogen in their cores, that are located in the instability strip. DS stars have short periods, 0.02 to 0.3 days, and absolute V magnitudes between 0 ≤ MV ≤ 4.4. -Long period variables (LPV) are stars that show variations with time scales on the order of months. These stars are normally red giant stars that are near the tip of the red giant, or asymptotic giant branch, and are experiencing thermal pulses. LPV light curves often show multiple variations going on at one time, not all of which are necessarily periodic. -Eclipsing binaries occur when two stars are in a binary, orbiting around their center of mass, and the plane of their orbit is such that the stars pass between each other from the point of view of an observer.
22 Chapter 4: Observations, Data Reduction, and Physical Property Determination
4.1 Observations and Image Processing
For this study I obtained observations of four globular clusters in the Large Magellanic Cloud (LMC): NGC 1466, NGC 1786, NGC 2210, and Reticulum. Observations were obtained with the SOAR Optical Imager (SOI) on the SOAR 4-m telescope and with ANDICAM on the SMARTS 1.3-m telescope. Table 4.1 gives the basic properties of the two instruments that were used. A quick summary of the number of observations, observation dates, and exposure times for each cluster is presented below.
Table 4.1: Properties of Instruments Used
Instrument Field of View (arcminutes) Pixel Scale (arcseconds/pixel)
SOI 5.2×5.2 0.153
ANDICAM 6×6 0.369
NGC 1466 - 40 V and 37 B images were obtained using SOAR in February and December of 2008. An additional 45 V and 43 B images were obtained using SMARTS from September 2006 to January 2007. Exposure times for the SOAR observations
23 were between 30s and 300s for V and between 60s and 300s for B, but were usually 120s and 180s for the V and B observations, respectively. SMARTS exposures were 450s for each filter. Reticulum - 38 V , 33 B, and 35 I images were obtained using SOAR in February of 2008 while an additional 45 V , 43 B, and 45 I images were obtained using SMARTS from September 2006 through the end of December 2006. SOAR exposure times were between 30s and 600s for V and I, and between 45s and 900s for B. SMARTS exposures were 450s for the V and B filters and 300s for the I filter. NGC 1786 - 48 V and 48 B images were obtained using SOAR in November of 2007 and February of 2008 while 43 V and 42 B images were obtained using SMARTS from September 2006 to January 2007. SOAR exposure times were between 30s and 600s for V and between 60s and 900s for B. SMARTS exposure times were 450s in each filter. NGC 2210 - 64 V , 61 B, and 61 I images were obtained using SOAR in February of 2008 while 45 images in V , B, and I were obtained using SMARTS from September 2006 to January 2007. SOAR exposure times were between 30 and 600s for V and I, and 45s and 900s for B. SMARTS exposure times were 450s for V and B, and 300s for I. The images from both telescopes were bias subtracted and flat-field corrected using IRAF1.
4.2 Photometry and Variable Identification
Stetson’s Daophot II/Allstar packages (Stetson, 1987, 1992, 1994) were run on the images in order to obtain instrumental magnitudes for each star. Observations of the Landolt standard fields PG0231, PG0942, PG1047, RU149, SA95, and SA98 (Landolt,
1IRAF is distributed by the National Optical Astronomical Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation.
24 1992) were used to determine a transformation from instrumental magnitudes to the standard system. This transformation was checked for each cluster by using standard stars within the cluster field or by comparing to previous photometry of that cluster. These checks are detailed in the chapters on the individual clusters. Daophot II/Allstar determines the brightness of stars by fitting a pseudo-Gaussian point spread function profile to each star. This works even when there is some blend- ing of stars as long as the program is able to fit a profile to each star. However, when the stars become so crowded and blended that it is not possible to fit a profile to each star, such as in the crowded centers of many clusters, the profile fitting technique fails. In order to locate variable stars in these extremely crowded regions, the SOAR data on the cluster centers were also searched using the ISISv2.2 image subtraction program (Alard, 2000). The light curves produced by ISIS are in relative fluxes. The V -band time series, which typically had more phase points than the B-band, was used to identify candidate variable stars using Peter Stetson’s Allframe/Trial package (Stetson, 1994). Period searches on the candidate variables were carried out using Supersmoother (Reimann, 1994), Period04 (Lenz & Breger, 2005), and a dis- crete Fourier transform (Ferraz-Mello, 1981) as implemented in the Peranso software suite2. The period phased light curves were visually inspected to confirm the validity of the variable stars. Light curves of candidate variable stars were then fit to template light curves (Layden, 1998) and checked by eye in order to confirm variable classifica- tion and period. The resulting primary periods are typically good to at least 0.0002 days (periods for the best observed stars are good to 0.00001 days); errors for the secondary periods of RRd stars are slightly worse, have an accuracy of approximately 0.0004 days. A similar search of the light curves produced with ISIS was done to find additional variables. 2http://www.peranso.com/
25 4.3 Determination of RR Lyrae Physical Prop- erties
One of the major goals of this study is to compare the physical properties of RR Lyrae stars in clusters of different Oosterhoff types in an effort to determine whether the processes that formed these stars differ with Oosterhoff type. Physical properties of RR Lyrae stars, such as mass, luminosity, and temperature; can be obtained through Fourier analysis of their light curves.
4.3.1 Fourier Decomposition
The RRab light curves were fit with a Fourier series of the form
n mag(t)= A0 + Aj sin(jωt + φj), (4.1) jX=1 where mag(t) is the magnitude as a function of time, Aj is the amplitude of each order, φj is a frequency offset, and ω =2π/P , where P is the pulsation period. The RRc light curves were fit in a similar fashion but a cosine series was used instead of the sine series. The Fourier fitting was done using a Fourier fitting code originally written by Geza Kov´acs (Kov´acs & Walker, 2001) with an analysis wrapper written by Nathan De Lee (De Lee 2011, in prep.). Error analysis for the Fourier decomposition parameters was done based on Petersen (1986). A number of fits were performed for each light curve, with a varying number of terms. The resulting Fourier series was then plotted on top of the original light curve and this was checked by eye to determine if the fit successfully reproduced the shape of the original light curve. Not all light curves were fit successfully, and the optimum number of terms to fit each individual light curve varied. Figure 4.1 shows an example of a failed and a successful Fourier series fit to a light curve.
26 Figure 4.1: Sample results of fitting a Fourier series to a light curve. The top panel shows an unsuccessful fit where too many terms were used, producing a ringing effect. The bottom panel shows a successful fit where the Fourier series does a good job of reproducing the shape of the original light curve.
4.3.2 RRab Variables
Jurcsik & Kov´acs (1996), Jurcsik (1998), and Kov´acs & Walker (1999,2001) provide formulae, determined empirically from observations of field RR Lyrae stars, for cal- culating the metallicity, [Fe/H], absolute magnitude, MV , and effective temperature, hV −Ki log Teff , of RRab stars using the Fourier coefficients from their V light curves. The stellar characteristics are determined using the following equations, which come
27 from equations (1), (2), (5), and (11) in Jurcsik (1998), respectively:
[Fe/H] = −5.038 − 5.394 P +1.345 φ31, (4.2)
MV =1.221 − 1.396 P − 0.477 A1 +0.103 φ31, (4.3)
(V − K)0 =1.585+1.257 P − 0.273 A1 − 0.234 φ31 +0.062 φ41, (4.4) and hV −Ki log Teff =3.9291 − 0.1112 (V − K)0 − 0.0032 [Fe/H]. (4.5)
The values for [Fe/H] derived through this method are in the scale of Jurcsik (1995), which can be transformed to the more common Zinn & West (1984) scale by the relation [Fe/H]J95 =1.431[Fe/H]ZW84 +0.880 (Jurcsik, 1995). The dereddened B −V and V − I color indices were calculated using equations (6) and (9) from Kov´acs & Walker (2001), which are reproduced here:
(B − V )0 =0.189 log P − 0.313 A1 +0.293 A3 +0.460 (4.6) and
(V − I)0 =0.253 log P − 0.388 A1 +0.364 A3 +0.648. (4.7)
The B − V and V − I color indices are also used to calculate effective temperatures via equations (11) and (12) in Kov´acs & Walker (2001),
hB−V i log Teff =3.8840 − 0.3219 (B − V )0 +0.0167 log(g)+0.0070 [M/H] (4.8) and
hV −Ii log Teff =3.9020 − 0.2451 (V − I)0 +0.0099 log(g) − 0.0012 [M/H], (4.9)
28 where g, the surface gravity of the star, is obtained from equation (12) in Kov´acs & Walker (1999),
log(g)=2.9383+ 0.2297 log(M/M⊙) − 0.1098 log Teff − 1.2185 log P, (4.10)
assuming a mass of M =0.7 M⊙.
4.3.3 RRc Variables
Simon & Clement (1993) demonstrated that the Fourier parameters of the V -band light curves of RRc stars could be used to calculate the mass, luminosity, temperature, and helium parameter for these stars. Unlike the empirically determined relationships between physical properties and Fourier parameters for RRab stars, the relationships for RRc stars were determined using light curves that were created with hydrodynamic pulsation models. These physical properties of RRc stars can be calculated using the equations:
log Teff =3.265 − 0.3026 log P − 0.1777 log M +0.2402 log L, (4.11)
log y = −20.26+4.935 log Teff − 0.2638 log M +0.3318 log L, (4.12)
log M =0.52 log P − 0.11 φ31 +0.39, (4.13)
and
log L =1.04 log P − 0.058 φ31 +2.41, (4.14)
which are equations (2), (3), (6), and (7) in Simon & Clement (1993), respectively. It should be noted that the helium abundance parameter, y, is not equal to the helium abundance, Y . It should also be noted that while these equations are commonly used in the literature, the equations for mass, luminosity, and temperature violate the
29 pulsation equation (Catelan, 2004b; Deb & Singh, 2010). While the values calculated for these properties cannot all be physically correct, they can be used for the purpose of making comparisons with the physical properties calculated the same way for RRc stars in other clusters. Empirically-motivated equations also exist for certain physical properties of RRc stars. Equation (10) in Kov´acs (1998),
MV =1.261 − 0.961 P − 0.044 φ21 − 4.447 A4, (4.15) allows the absolute magnitude for the RRc stars to be calculated. The metallicity in the Zinn & West (1984) scale can be calculated using equation (3) from Morgan, Wahl, & Wieckhorst (2007):
2 2 [Fe/H]ZW84 = 52.466 P − 30.075 P +0.131 φ31
+0.982 φ31 − 4.198 φ31P +2.424. (4.16)
It has been noted in the literature that RRc masses calculated using the Simon
& Clement (1993) equations can at times be too small, ≃ 0.5M⊙, which approaches the mass of a degenerate helium core at the helium flash (Corwin et al., 2003). This is likely due to a problem with the equations used but still produces values that are suitable for comparison purposes in this dissertation.
30 Chapter 5: NGC 1466
NGC 1466 is an old globular cluster that is located relatively far from the center of the LMC. The cluster has a metal abundance of [Fe/H] ≈ −1.60 and is not very reddened, E(B-V) = 0.09 ± 0.02 (Walker, 1992b). Johnson et al. (1999) used color- magnitude diagrams obtained with the Hubble Space Telescope to determine that the age of NGC 1466 is within 1 Gyr of the ages of the Milky Way globular clusters M3 (NGC 5272) and M92 (NGC 6341), showing that NGC 1466 is as old as the oldest Galactic halo clusters. NGC 1466 features a well-populated horizontal branch that extends through the instability strip (see Figure 5 in Walker (1992b)); thus it is expected to contain a significant number of RR Lyrae stars. RR Lyrae stars were first found in NGC 1466 by Thackeray & Wesselink (1953), and more RR Lyrae were discovered by Wesselink (1971). The most recent study of variable stars in NGC 1466 was conducted by Walker (1992b), who found 42 RR Lyrae stars; 25 RRab stars and 17 RRc’s. Due to the density of unresolved stars in the cluster core, Walker did not perform photometry of stars within a radius of 13 arcsec from the cluster center, suggesting that there are probably additional RR Lyrae stars that could not be detected. The core radius of NGC 1466 is 10.7±0.4 arcsec, as measured by Mackey & Gilmore (2003) using images from the Hubble Space Telescope, which is entirely within the region of the cluster where Walker was unable to perform photometry. Advances in instrument resolution and image-subtraction techniques now make it easier for us to search for variable
31 stars in more crowded regions. From my observations, I obtained a total of 85 V and 80 B images of NGC 1466 which represents a larger data set than the 35 BV pairs obtained by Walker. This increase in time series photometry will improve the chances of identifying new variable stars and obtaining better sampled light curves.
14 RRab RRc 15 RRd LPV 16 AC
17
18
V 19
20
21
22
23
-0.5 0 0.5 1 1.5 2 B-V
Figure 5.1: V ,B − V CMD for NGC 1466. Different variable stars of interest are indicated as follows: RRab: plus sign, RRc: filled triangle, RRd: filled circle, and long period variable stars: filled squares. The potential Anomalous Cepheid is indicated by an open triangle.
5.1 Data Reduction for NGC 1466
Data reduction was primarily carried out following the method described in Chapter 4. Howerever, as noted in Walker (1992b), NGC 1466 is located near two very bright stars which create problems with scattered light across some of the images, especially in many of the images obtained with the SMARTS telescope. The procedure described
32 18.5
19
V 19.5
20
RRab RRc RRd 20.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 B-V
Figure 5.2: V ,B − V CMD for NGC 1466 that is zoomed in on the horizontal branch. The symbols used are the same as in Figure 5.1 by Stetson & Harris (1988) was used to remove this scattered light; this was the same method employed by Walker (1992b). The Daophot II/Allstar packages (Stetson, 1987, 1992, 1994) were used to locate, measure, and subtract stars from all images. The subtracted images were then smoothed using a 40x40 pixel median filter. The average sky level in the smoothed images was determined and then the smoothed images were subtracted from the original images. The average sky values were then added back into the new images, creating a final set of images with a constant sky background. Johnson et al. (1999) showed the photometry in Walker (1992b) to be in good agreement with HST/WFPC2 observations of NGC 1466, ∆V = 0.008 ± 0.02, after these observations were transformed from the on-board HST system to the standard
33 Johnson-Cousins system. I compared the results of the initial transformation to the standard system, calibrated using observations of Landolt standard fields, to Walker’s photometry of isolated non-variable stars across a range of brightnesses within the cluster. Small corrections were made to the zero points and color terms from the initial transformation equations in order to achieve better agreement with Walker’s photometry. This produced an average difference between my data and Walker’s of ∆V =0.012 ± 0.012 and ∆B =0.026 ± 0.020. This is a similar level of deviation to that obtained by Johnson et al. (1999) in their comparison with Walker. The center of NGC 1466 is too crowded for profile fitting photometry to be ac- curately performed and thus the results from ISIS were relied on in order to identify variables in the most crowded portion of the cluster. Four of the variable stars were found only by ISIS (V31,V51, V54, V60). These stars are located deep in the cluster center and are too crowded to obtain accurate profile fitting photometry. These four light curves are shown in relative fluxes; for the other variables their light curves obtained from Daophot II/Allstar are presented.
5.2 Variable Stars
A total of 62 variables were found, including 49 RR Lyraes, 1 additional candidate RR Lyrae, 2 long-period variables, a candidate Anomalous Cepheid, and 9 variables of unknown classification. As described below, double-mode (RRd) variables in the RR Lyrae population of NGC 1466 were able to be identified for the first time. Of the confirmed RR Lyrae stars, 30 were RRab stars, 11 were RRc stars, and 8 were RRd type. The RRd variable stars are discussed separately in section 5.2.3. Figures 5.3, 5.4, and 5.5 show sample light curves for the RRab, RRc, and RRd stars; the full set of light curves for all of the variable stars in NGC 1466 can be found in Appendix A. Table 5.1 lists the variable stars and their coordinates, classification, and period, while Table 5.2 gives the photometric properties (V and B amplitudes, intensity-
34 Figure 5.3: Sample light curve for the RRab stars in NGC 1466. The top panel shows the V -band light curve while the B-band light curve is shown in the bottom panel. The full set of light curves can be found in Appendix A. weighted V and B mean magnitudes, and magnitude-weighted mean B −V color) for the variable stars, except for the RRd stars.. Notes on some of the individual stars are in the following subsections. Table 5.3 contains a sample of the photometric data for the variable stars, the full version can be found in Kuehn et al. (2011). I use a naming system that is an extension of the one used in Wesselink (1971). All variables are named in the form of Vxx, with stars up through V42 being ones that were originally found by Wesselink. A cross identification of the naming system used by Walker and my variable star numbers is included in Table 5.2.
35 Figure 5.4: Sample light curve for the RRc stars in NGC 1466. The full set of light curves can be found in Appendix A.
36 0.6 P_0 V 18.8 0.4 19 0.2 19.2 0 19.4 -0.2 19.6 -0.4 19.8 0.6 P_1 B 19.2 0.4 19.4 0.2 19.6 0 19.8 -0.2 20 -0.4 20.2
0 0.5 1 1.5 2 0 0.5 1 1.5 2 Phase Phase
Figure 5.5: Sample light curve for the RRd stars in NGC 1466. The right-hand panels show the raw light curves, as plotted with the first overtone mode period (the first overtone amplitude is larger than the fundamental mode amplitude for all RRd stars in NGC 1466), while the left-hand panels show the deconvolved V light curves. The full set of light curves can be found in Appendix A.
37 Table 5.1: Variable Stars in NGC 1466
ID RA(J2000) DEC(J2000) Type P (days) Other IDs
V1 03:44:44.7 −71:40:44.9 RRab-BL 0.55035 Wa415 V2 03:44:27.4 −71:40:59.7 RRd 0.4751 Wa124 V3 03:44:20.2 −71:40:00.2 RRd 0.4717 Wa66 V4 03:44:20.3 −71:39:57.1 RRab-BL 0.57239 Wa67 V5 03:44:26.6 −71:39:48.9 RRab 0.57863 Wa108 V6 03:44:30.8 −71:39:54.8 RRab-BL 0.52805 Wa182 V7 03:44:28.4 −71:39:13.3 RRd 0.4859 Wa135 V8 03:44:26.3 −71:40:06.5 RRab-BL 0.51970 Wa106 V9 03:44:26.7 −71:40:17.2 RRab 0.52260 Wa109 V10 03:44:27.4 −71:40:19.0 RRd 0.4730 V12 03:44:28.9 −71:40:15.0 RRab Wa146 V13 03:44:33.8 −71:40:48.1 RRc 0.33936 Wa262 V14 03:44:36.2 −71:40:48.7 RRab-BL 0.56414 Wa320 V15 03:44:35.4 −71:40:44.2 RRab 0.56708 Wa303 V16 03:44:34.9 −71:40:45.1 RRab 0.69427 Wa290 V18 03:44:26.7 −71:40:14.5 ? 0.48 Wa110 V19 03:44:47.1 −71:40:39.8 RRab 0.61620 Wa426 V20 03:44:30.7 −71:41:22.5 RRab 0.59084 Wa183 V21 03:44:51.9 −71:39:53.4 RRab 0.52150 Wa448 V22 03:44:35.5 −71:41:05.7 RRc 0.33081 Wa301 V23 03:44:38.6 −71:41:24.7 RRab 0.49342 Wa361 V24 03:44:19.9 −71:41:25.5 RRd 0.4938 Wa65 V25 03:44:36.4 −71:39:53.9 RRd 0.4715 Wa323 V26 03:44:34.2 −71:40:51.4 RRab 0.51364 Wa274
38 Table 5.1 (continued)
ID RA(J2000) DEC(J2000) Type P (days) Other IDs
V28 03:44:21.3 −71:40:38.1 RRc 0.32039 Wa71 V29 03:44:15.5 −71:40:11.9 RRd 0.4824 Wa53 V30 03:44:31.3 −71:39:52.0 RRab 0.69445 Wa194 V31 03:44:32.1 −71:39:50.5 ? 0.34272 V32 03:44:29.4 −71:40:13.7 AC? 0.49661 V33 03:44:29.0 −71:40:43.9 RRc 0.27841 Wa148 V34 03:44:28.0 −71:39:60.0 ? 0.61549 Wa129 V35 03:44:29.7 −71:40:42.5 RRab-BL 0.58172 Wa164 V38 03:44:49.0 −71:40:48.7 RRc 0.34858 Wa437 V39 03:44:30.6 −71:40:07.2 RRab 0.56248 Wa179 V40 03:44:31.0 −71:40:01.1 RRab 0.53606 Wa185 V41 03:44:39.4 −71:40:21.3 RR? V42 03:44:30.4 −71:41:00.6 RRab 0.63482 Wa177 V44 03:44:22.0 −71:38:13.1 RRab Wa75,S27 V45 03:44:23.1 −71:41:16.0 RRc 0.31043 Wa82,S27 V46 03:44:27.4 −71:39:14.0 RRab 0.68909 Wa121 V47 03:44:28.9 −71:40:27.8 RRd 0.4733 V48 03:44:29.4 −71:40:00.0 RRc 0.37697 Wa153,S3 V49 03:44:30.2 −71:40:09.5 RRab 0.68635 V50 03:44:31.1 −71:40:28.7 RRab-BL 0.58194 V51 03:44:31.6 −71:40:12.7 ? 0.35892 V52 03:44:31.6 −71:40:34.6 RRc V53 03:44:31.9 −71:40:15.8 LP V54 03:44:32.1 −71:40:12.9 ? 0.55608 V55 03:44:32.5 −71:40:13.3 RRab-BL 0.60951
39 Table 5.1 (continued)
ID RA(J2000) DEC(J2000) Type P (days) Other IDs
V56 03:44:33.4 −71:40:01.8 RRab 0.62238 V57 03:44:33.5 −71:39:51.7 RRc 0.35692 Wa249,S29 V58 03:44:33.5 −71:39:59.0 RRab 0.56752 V59 03:44:33.7 −71:40:20.2 ? V60 03:44:33.9 −71:40:11.4 AC?,RRab? 0.52210 V61 03:44:33.9 −71:40:01.7 RRab-BL 0.66927 V62 03:44:35.5 −71:40:35.8 ? 0.50414 V63 03:44:35.6 −71:39:54.0 RRab 0.58760 Wa306,S31 V64 03:44:38.4 −71:40:39.5 RRab 0.68767 Wa356,S30 V65 03:44:39.0 −71:40:03.7 LP V66 03:44:40.0 −71:41:10.3 RRc 0.33633 Wa382,S17 V67 03:44:45.1 −71:42:13.1 ? V68 03:44:56.5 −71:38:54.3 RRc 0.34914 Wa458
Table 5.2: Photometric Parameters for Variables in NGC 1466, Excluding RRd Stars
ID Type P (days) AV AB hV i hBi hB − V i Other IDs V1 RRab-BL 0.55035 0.64 0.77 19.380 19.793 0.421 Wa415 V4 RRab-BL 0.57239 0.87 1.16 19.406 19.804 0.425 Wa67 V5 RRab 0.57863 0.67 0.82 19.391 19.781 0.403 Wa108 V6 RRab-BL 0.52805 1.19 1.49 19.290 19.672 0.410 Wa182 V8 RRab-BL 0.51970 0.89 1.2 19.273 19.599 0.358 Wa106 V9 RRab 0.52260 1.24 1.52 19.414 19.743 0.362 Wa109 V12 RRab Wa146
40 Table 5.2 (continued)
ID Type P (days) AV AB hV i hBi hB − V i Other IDs V13 RRc 0.33936 0.55 0.69 19.298 19.564 0.276 Wa262 V14 RRab-BL 0.56414 0.93 1.29 19.402 19.803 0.421 Wa320 V15 RRab 0.56708 0.81 1.05 19.209 19.675 0.487 Wa303 V16 RRab 0.69427 0.53 0.69 19.360 19.817 0.466 Wa290 V18 ? 0.48 0.15 0.29 18.903 20.168 1.268 Wa110 V19 RRab 0.61620 0.61 0.79 19.360 19.785 0.435 Wa426 V20 RRab 0.59084 1.05 1.33 19.280 19.648 0.396 Wa183 V21 RRab 0.52150 1.22 1.54 19.315 19.632 0.359 Wa448 V22 RRc 0.33081 0.51 0.65 19.200 19.543 0.353 Wa301 V23 RRab 0.49342 1.25 1.51 19.291 19.681 0.421 Wa361 V26 RRab 0.51364 1.03 1.38 19.339 19.702 0.400 Wa274 V28 RRc 0.32039 0.57 0.7 19.338 19.652 0.324 Wa71 V30 RRab 0.69445 0.66 0.91 19.273 19.677 0.421 Wa194 V31 ? 0.34272 V32 AC? 0.49661 0.42 0.70 18.118 18.614 0.505 V33 RRc 0.27841 0.51 0.57 19.355 19.600 0.247 Wa148 V34 ? 0.61549 0.31 0.45 18.194 18.896 0.709 Wa129 V35 RRab-BL 0.58172 0.6 0.78 19.248 19.668 0.432 Wa164 V38 RRc 0.34858 0.44 0.54 19.354 19.682 0.335 Wa437 V39 RRab 0.56248 1.12 1.37 19.156 19.538 0.407 Wa179 V40 RRab 0.53606 Wa185 V41 RR? 0.59 19.598 V42 RRab 0.63482 0.51 0.66 19.384 19.865 0.489 Wa177 V44 RRab Wa75,S27 V45 RRc 0.31043 0.38 0.49 19.233 19.503 0.275 Wa82,S27
41 Table 5.2 (continued)
ID Type P (days) AV AB hV i hBi hB − V i Other IDs V46 RRab 0.68909 0.38 0.49 19.352 19.813 0.466 Wa121 V48 RRc 0.37697 0.44 0.54 19.288 19.580 0.316 Wa153,S3 V49 RRab 0.68635 0.53 0.7 19.255 19.773 0.528 V50 RRab-BL 0.58194 1.05 1.24 19.444 19.778 0.356 V51 ? 0.35892 V52 RRc V53 LP V54 ? 0.55608 V55 RRab-BL 0.60951 V56 RRab 0.62238 0.73 0.96 19.189 19.701 0.527 V57 RRc 0.35692 0.42 0.5 19.295 19.685 0.395 Wa249,S29 V58 RRab 0.56752 1.05 1.28 19.368 19.905 0.570 V59 ? 0.460.5418.19418.651 0.460 V60 AC?,RRab? 0.52210 V61 RRab-BL 0.66927 0.86 1.13 19.510 19.985 0.497 V62 ? 0.50414 0.71 1.08 18.758 19.266 0.531 V63 RRab 0.58760 0.82 0.99 19.415 19.890 0.490 Wa306,S31 V64 RRab 0.68767 0.49 0.59 19.307 19.809 0.508 Wa356,S30 V65 LP V66 RRc 0.33633 0.52 0.67 19.277 19.608 0.342 Wa382,S17 V67 ? V68 RRc 0.34914 0.47 0.65 19.410 19.749 0.348 Wa458
42 Table 5.3: Sample Photometry of the Variable Stars
ID Filter JD Phase Mag Mag Error
V01 V 2453980.8494 0.13881 19.252 0.034
V01 V 2453987.7614 0.69800 19.841 0.105 V01 V 2453991.7381 0.92371 19.199 0.052
V01 V 2453994.7980 0.48359 19.552 0.035 V01 V 2453996.7729 0.07200 19.350 0.042
5.2.1 RR Lyrae Stars
I found 41 of Walker’s (1992) 42 RR Lyrae stars along with 6 new RRab stars, 1 new RRc, and 2 new RRd stars. Six of the previously identified RR Lyrae stars in NGC 1466 were reclassified as RRd stars. I was unable to find Walker’s variable 145, which appears to be a blend of two stars in my images, neither of which displays variability. The additional RR Lyrae stars are all located in the central region of the cluster. The RRab stars have intensity-weighted mean magnitudes of hV i = 19.331 ± 0.016 and hBi = 19.751 ± 0.020, while the mean magnitudes for the RRc stars are hV i = 19.305 ± 0.019 and hBi = 19.617 ± 0.023. Walker found hV i = 19.33 ± 0.02 and hBi = 19.71 ± 0.02 for the RRab stars while the RRcs had hV i = 19.32 ± 0.02 and hBi = 19.62 ± 0.02, which are in good agreement with my results. The stars with a large discrepancy from Walker’s photometry are discussed in detail in subsection 5.2.2. There were no significant differences between my periods and those calculated by Walker (1992b). V33 was the only star, that did not turn out to be a misclassified RRd, to display a difference in period greater than 0.01 days. Walker found a period
43 of 0.38250 days while I found a period of 0.27841 days. A period search was run on Walker’s light curve for this star and a secondary signal for a period around 0.27 days was found, suggesting that this disagreement in periods is due to aliasing in Walker’s light curve. The accuracy of the periods determined by both Walker and myself is not high enough to allow for the identification of any change in period for the RR Lyrae stars.
5.2.2 Comments on Individual RR Lyrae Stars
V18, Walker 110, is listed as an unclassified variable. V18 is slightly brighter than the horizontal branch but is very red, B − V =1.27. It has a period of 0.48 days and an amplitude of 0.15 mag in V . Walker (1992b) noted that in his images this star had an elongated shape that suggested an unresolved companion. My images also show this star to be elongated. Periods were unable to be determined for V44 (Walker 75) and V12 (Walker 146) due to not having enough data points for accurate period determination. These two RRab stars were not detected in all images, but the shape of the partial light curves is entirely consistent with their classification as RRab stars. V41 was classified only as a candidate RR Lyrae star due to aliasing issues which prevented us from determining a period or classification as RRab or RRc. Walker (1992b) was unable to measure this star due to its proximity to a brighter star. Not enough observations were obtained to definitively determine if any of the RR Lyrae stars have the Blazhko effect. However, based on the scatter in their light curves, V1, V4, V6, V8, V14, V35, and V50 are potential Blazhko stars. V55 and V61 also show scatter in their light curves that could be due to the Blazhko effect, but these two stars are located in the crowded region near the cluster center so the scatter could also be due to contamination. V40 features a light curve that has a fair amount of scatter as well as a shape that
44 is unusually symmetric for an RRab star. Despite its unusual shape, the light curve was best fit with a period of 0.536 days and thus is tentatively classified as an RRab.
5.2.3 RRd Stars
The increased number of observations (over Wesselink (1971) Walker (1992b)) allowed for the identification of eight RRd stars in NGC 1466. Table 5.4 lists the identified RRd stars, their fundamental mode and first overtone periods (in days) and ampli- tudes, and their period ratios. Periods were calculated using the period04 program (Lenz & Breger, 2005). The periods are typically good to ±0.0001 or 0.0002 days. Six of the RR Lyrae identified by Walker (1992b) turned out to be RRd stars. Five were originally identified as RRc stars and one as an RRab. V2, V3, V24, and V25 all have first overtone periods that agree with the RRc period that was found by Walker. V7 was previously classified as an RRc with a period of 0.34925 days; however, a first overtone period of 0.3615 days was obtained. Walker classified V29 as an RRab star with a period of 0.56030 days, which does not correspond with either the fundamental or first overtone period that I found.
Table 5.4: Photometric Parameters for the RRd Variables in NGC 1466
ID Type P0 (d) P1 (d) P1/P0 AV,0 AV,1 AB,0 AB,1 hV i hBi hB − V i V2 RRd 0.4751 0.3534 0.7451 0.12 0.42 0.15 0.53 19.375 19.758 0.389 V3 RRd 0.4717 0.3505 0.7431 0.13 0.41 0.15 0.53 19.368 19.779 0.416 V7 RRd 0.4859 0.3615 0.7440 0.35 0.43 0.42 0.52 19.326 19.642 0.310 V10 RRd 0.4730 0.3518 0.7437 0.26 0.48 0.30 0.52 19.425 19.797 0.370 V24 RRd 0.4938 0.3675 0.7442 0.12 0.43 0.15 0.60 19.292 19.642 0.357 V25 RRd 0.4715 0.3508 0.7440 0.20 0.44 0.40 0.65 19.360 19.705 0.350 V29 RRd 0.4824 0.3589 0.7440 0.45 0.58 0.36 0.38 19.428 19.750 0.320 V47 RRd 0.4733 0.3519 0.7435 0.42 0.58 0.48 0.60 19.410 19.760 0.350
45 Of the two new RRd stars, V10 was thought to be a potential variable by Wesselink (1971). Walker (1992b) did not classify this star as a variable due to its proximity to a blue HB star, which made observations difficult. Figure 5.6 shows the ratio of the first overtone period to the fundamental mode period vs fundamental period, Petersen diagram (Petersen, 1973), for the RRd stars in NGC 1466; the RRd stars in the LMC field (Soszy´nski et al., 2003) are also plotted. The NGC 1466 RRd stars fall in the same area of the Petersen diagram as the majority of the LMC field stars. This is the same region where RRd stars in Milky Way Oosterhoff-I clusters tend to fall (see, e.g., Fig. 1 in Popielski et al. (2000), and Fig. 13 in Clementini et al. (2004)).
5.2.4 Other Variables
Two long-period variables, V53 and V65, were found in NGC 1466. Periods were unable to be determined for either of these stars; in fact, I do not have observations of them over a long enough period of time to say for sure that their variability is periodic. Both stars are located near the tip of the giant branch on the CMD, as can be seen in Figure 5.1, and have several possible period solutions in the range of 60 to 90 days. V32 (Fig. 5.7) appears to be a potential Anomalous Cepheid (AC), having an average V luminosity that is approximately 1.2 magnitudes brighter in V than the RR Lyrae stars. The star has a possible period of either 0.331 days or 0.497 days. The 0.497 day period would be consistent with the period-luminosity diagram for ACs from Pritzl et al. (2005a). Based on Equations 2 through 5 in Pritzl et al. (2002) and the distance modulus that I derive for NGC 1466 from the RR Lyrae stars, V32 would most likely be a first overtone pulsator. If the 0.331 day period is correct, the star would be too bright to be an AC, based on the period-luminosity diagram,
46 0.75 LMC Field NGC 1466
0.748
0.746 P1/P0 0.744
0.742
0.74 0.42 0.44 0.46 0.48 0.5 0.52 0.54 0.56 0.58 0.6 Fundamental Period (days)
Figure 5.6: Petersen diagram showing the ratio of the first overtone period to the fundamental mode period vs. fundamental mode period for the RRd stars in the cluster (blue triangles). Also plotted are the RRd stars in the LMC field (red plus symbols) from Soszy´nski et al. (2003). and would most likely be a foreground RR Lyrae. The shape of V32’s light curve is similar to an RRab star, which would be inconsistent with a 0.331 day period. Based on this I feel that the 0.497 day period is correct and that this star is either an AC or, less likely, a foreground RRab. Nine variables of unknown classification were found. Of these stars, 4 were only found by ISIS as they were either located in the crowded cluster center (V31, V51, and V54) or near the bright star in the southeast corner of the images (V67). Thus their light curves are in differential fluxes, which does not allow positive classifications to be obtained. While periods and light curve shape can be used to determine potential classifications, without having a magnitude it is not possible to distinguish between
47 Figure 5.7: Light curve for the potential Anomalous Cepheid in NGC 1466. a cluster RR Lyrae, a foreground RR Lyrae, or an AC. Notes on the other stars with unknown classification follow. - V34 (Walker 129) is about one magnitude brighter than the horizontal branch and has a B − V = 0.70. Wesselink (1971) had labeled this star as a variable but Walker (1992b) considered it a constant RHB star. The period, 0.61594 days, and light curve shape of this star suggest that it could be an RRab star whose color and brightness are affected by contamination. - Star V59 is located in the cluster center and has an ISIS light curve that suggests several possible periods. The light curves from Daophot photometry suggest that it has a similar color to the RR Lyrae stars but is about one magnitude brighter; this is possibly due to contamination, but V59 displays a B to V amplitude ratio that is similar to the other RR Lyraes in the cluster (Fig. 5.8). V59 could also potentially
48 be an AC or a Type II Cepheid.
1.3
1.2
1.1
1
0.9
0.8
V Amplitude 0.7 V62
0.6
0.5 V59
0.4
0.3 0.4 0.6 0.8 1 1.2 1.4 1.6 B Amplitude
Figure 5.8: V vs B amplitudes for the RRab stars (plus symbols) and RRc stars (crosses). Also plotted are two of the variables of unknown classification (labeled squares) for purposes of determining if they are RR Lyrae stars that are affected by blending. V59 follows the trend of the RR Lyrae stars, suggesting that it is not blended, while V62 departs from this trend, supporting the explanation that it is blended (see discussion in section 3.3). The plotted line shows the relationship between V and B amplitudes for NGC 2257 (Nemec et al., 2009), an Oo-int globular cluster in the LMC. The agreement between this line and the RR Lyrae stars in NGC 1466 suggests a similarity between Oo-int globular clusters, though we cannot rule out that this relationship exists regardless of Oosterhoff type.
- V60 is located in the crowded cluster center and has a clean ISIS light curve that suggests a period of 0.522 days. The light curve from Daophot suggests a luminosity approximately two magnitudes brighter than the RR Lyrae stars but the light curve is messy, possibly due to blending. - Star V62 is located in the cluster center and has a light curve that suggests that it is a variable with a period near 0.5 days. The period and the light curve shape suggest that V62 is possibly an RR Lyrae but the light curve is messy and it is
49 brighter than the other RR Lyrae stars, likely due to contamination by nearby stars. The contamination explanation is supported by the fact that V62 has a B amplitude that is slightly too large for its V amplitude, compared to the RR Lyrae stars in NGC 1466 (Fig. 5.8.
5.3 Physical Properties of the RR Lyrae Stars
Physical properties for the RR Lyrae stars were determined using the Fourier de- composition parameters with the empirical relations described in Chapter 4. For this Fourier decomposition analysis, 13 RRab and 7 RRc light curves were used.
Tables 5.5 and 5.6 give the amplitude ratios, Aj1 = Aj/A1, and phase differences,
φj1 = φj − jφ1, for the low-order terms (j = 2, 3, 4), and the number of terms used in the Fourier fit, for the RRab and RRc stars, respectively. For the RRab stars, the
Jurcsik-Kov´acs Dm value (Jurcsik & Kov´acs, 1996) is also listed. The Dm value helps to separate RRab stars with “regular” light curves from those with “anomalous” light curves, with lower Dm values representing more “regular” light curves. Tables 5.7 and 5.8 give the physical properties of the RRab and RRc stars, respectively.
Table 5.5: Fourier Coefficients for RRab Variables
ID A1 A21 A31 A41 φ21 φ31 φ41 Dmax Order V4 0.346 0.498 0.301 0.155 2.16 4.77±0.18 1.12 30.46 8 V5 0.243 0.380 0.361 0.206 2.31 5.12±0.21 1.69 49.89 8 V6 0.422 0.322 0.303 0.174 2.68 5.30±0.27 1.83 9.62 6 V8 0.349 0.402 0.324 0.194 2.47 5.02±0.37 1.39 40.96 7 V9 0.463 0.416 0.244 0.099 2.30 4.52±0.17 1.10 7.63 7 V14 0.355 0.440 0.351 0.205 2.25 4.84±0.14 1.34 14.33 9 V19 0.252 0.432 0.177 0.117 1.94 4.93±0.37 1.17 6.53 7 V20 0.363 0.502 0.356 0.271 2.26 4.99±0.09 1.26 45.97 6
50 Table 5.5 (continued)
ID A1 A21 A31 A41 φ21 φ31 φ41 Dmax Order V23 0.424 0.456 0.361 0.237 2.25 4.66±0.08 1.04 47.39 10 V26 0.367 0.369 0.249 0.139 2.26 4.80±0.19 0.78 34.99 7 V30 0.232 0.457 0.305 0.153 2.36 5.22±0.34 1.93 23.20 10 V42 0.204 0.411 0.251 0.098 2.46 5.51±0.16 2.20 10.83 10 V56 0.276 0.400 0.282 0.135 2.50 5.38±0.12 1.67 5.31 8
Table 5.6: Fourier Coefficients for RRc Variables
ID A1 A21 A31 A41 φ21 φ31 φ41 Order V22 0.272 0.179 0.085 0.067 4.67 2.55±0.30 0.89 6 V28 0.276 0.252 0.103 0.126 4.73 3.15±0.37 1.55 6 V33 0.246 0.255 0.039 0.011 4.38 2.72±0.75 4.95 8 V38 0.228 0.114 0.064 0.028 4.58 4.16±0.57 1.74 6 V45 0.199 0.090 0.042 0.055 4.41 2.71±0.79 1.53 6 V57 0.222 0.139 0.080 0.045 4.71 3.97±0.60 2.01 7 V66 0.259 0.181 0.090 0.033 4.30 3.93±0.54 3.24 9
Table 5.7: Derived Physical Properties for RRab Variables
hV −Ki hB−V i hV −Ii ID [Fe/H]J95 hMV i hV − Ki log Teff hB − V i log Teff log Teff V4 -1.717 0.748 1.164 3.805 0.336 3.810 3.811 V5 -1.278 0.824 1.153 3.805 0.365 3.804 3.802 V6 -0.764 0.828 1.008 3.819 0.313 3.825 3.818
51 Table 5.7 (continued) hV −Ki hB−V i hV −Ii ID [Fe/H]J95 hMV i hV − Ki log Teff hB − V i log Teff log Teff V8 -1.085 0.846 1.054 3.815 0.330 3.817 3.813 V9 -1.774 0.736 1.125 3.810 0.295 3.824 3.825 V14 -1.577 0.762 1.149 3.806 0.338 3.811 3.811 V19 -1.725 0.749 1.209 3.800 0.354 3.804 3.805 V20 -1.511 0.737 1.139 3.807 0.341 3.810 3.810 V23 -1.434 0.810 1.064 3.815 0.314 3.821 3.819 V26 -1.359 0.823 1.057 3.816 0.317 3.820 3.818 V30 -1.759 0.679 1.292 3.791 0.378 3.795 3.797 V42 -1.056 0.805 1.175 3.802 0.374 3.802 3.799 V56 -1.155 0.775 1.136 3.806 0.357 3.807 3.804
Mean -1.400 0.779 1.133 3.808 0.339 3.812 3.810 σ 0.088 0.013 0.021 0.002 0.007 0.003 0.002
Table 5.8: Derived Physical Properties for RRc Variables
ID [Fe/H]ZW84 hMV i M/M⊙ log(L/L⊙) log Teff Y V22 -1.970 0.657 0.724 1.762 3.859 0.254 V28 -1.669 0.591 0.611 1.713 3.864 0.272 V33 -1.420 0.788 0.633 1.675 3.871 0.281 V38 -1.419 0.696 0.495 1.693 3.864 0.284 V45 -1.764 0.720 0.672 1.724 3.864 0.266 V57 -1.614 0.666 0.526 1.715 3.862 0.276 V66 -1.425 0.711 0.515 1.690 3.865 0.283
Mean -1.612 0.690 0.597 1.710 3.86 0.274
52 table 5.8 (continued)
ID [Fe/H]ZW84 hMV i M/M⊙ log(L/L⊙) log Teff Y σ 0.079 0.023 0.033 0.011 0.001 0.004
The mean metallicity of the NGC 1466 RRab stars is [Fe/H]J95 = −1.40 ± 0.09 which in the Zinn & West scale is [Fe/H]ZW84 = −1.59±0.06. The mean metallicity of
the RRc stars is [Fe/H]ZW84 = −1.61±0.08, which is in good agreement with the value obtained for the RRab stars. Previously published metallicities for NGC 1466 showed a wide range of values. Olszewski et al. (1991) reported a metallicity of [Fe/H]= −2.17 based on spectroscopic observations of the calcium triplet in two giant stars in the cluster whose individual metallicities were [Fe/H]= −1.85 and −2.48. Walker (1992b) argued that the more metal-poor of these two stars was not a cluster member, and instead reported the cluster metallicity was [Fe/H]= −1.85, which is based on the remaining star from Olszewski et al. Walked reported that this metallicity was supported by comparisons of the RR Lyrae stars and the cluster CMD to that of other clusters. Wolf et al. (2007) used stellar popular synthesis models to find metallicities of [Fe/H]= −1.30 and −2.00, depending on whether they used the full spectrum or just the CN spectrum. A more metal poor result of [Fe/H]= −2.25 was adopted by Mackey & Gilmore (2003) for their work with cluster surface brightness profiles. A far more metal rich value of [Fe/H]= −1.64 was found by Santos & Piatti (2004) using the equivalent widths of metal lines in integrated spectra. My value of [Fe/H]= −1.59 is most consistent with the Santos & Piatti result.
5.4 Distance Modulus
The absolute magnitude for the RR Lyrae stars is obtained by using the abso- lute magnitude-metallicity relation for RR Lyrae stars by Catelan & Cort´es (2008).
53 The average of the Fourier derived metallicities for the RRab and RRc stars is
[Fe/H]ZW84 = −1.60 ± 0.05, which gives an absolute magnitude of MV =0.62 ± 0.14. The average apparent magnitude of the RRab and RRc stars are hV i = 19.331 ± 0.02 and hV i = 19.305 ± 0.02, respectively. Since the average magnitude for the RRab and RRc stars are essentially the same, I combine them for the purpose of calculating the distance, resulting in an average magnitude of hV i = 19.324 ± 0.013. Using the reddening value of E(B − V )=0.09 ± 0.02 from Walker (1992b) and a standard
extinction law with AV /E(B − V )=3.1, a reddening-corrected distance modulus of
(m − M)0 = 18.43 ± 0.15 is obtained. This distance modulus is approximately equal
to the distance modulus of (m−M)LMC = 18.44±0.11 that Catelan & Cort´es (2008) derived for the LMC.
5.5 Oosterhoff Classification
The average periods for the RR Lyrae stars in NGC 1466 are hPabi =0.591 days and
hPci =0.335 days. I found 30 RRab, 11 RRc, and 8 RRd stars, giving the cluster a
Nc+d/Nc+d+ab = 0.39. All three of these values are consistent with an Oosterhoff- intermediate (Oo-int) classification for NGC 1466. The minimum period for RRab stars has also been shown to be a good indicator of Oosterhoff class. NGC 1466 has
a minimum period for RRab stars of Pab,min =0.4934 days, which is consistent with it being an Oo-int object (Section 9.2). Another indicator of Oosterhoff status is the position of the RR Lyrae stars in the Bailey diagram. Figures 5.9 and 5.10 show the Bailey (period-amplitude) diagrams for NGC 1466 for both the V -band amplitudes and B-band amplitudes. The typical location of the RRab and RRc stars in Oosterhoff I (Oo-I) and II (Oo-II) clusters are indicated by red and green lines, respectively (Cacciari et al., 2005; Zorotovic et al., 2010). In both diagrams the RRab stars display a wide scatter. Many are located between the Oo-I and O-II loci, which is consistent with an Oo-int object. However,
54 there is a significant number of RRab stars that are clustered around the Oo-I line, which is more typical for an Oo-I object. The RRc stars fall almost exclusively between the reference lines, as is expected for an Oo-int object.
OoI 1.4 OoII RRab, large Dm RRab, small Dm RRab, no Dm 1.2 RRc RRd
1 V A 0.8
0.6
0.4
0.2 -0.5 -0.45 -0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05
log(Pdays)
Figure 5.9: Bailey diagram, log period vs V -band amplitude, for the RR Lyrae stars in NGC 1466. Red and green lines indicate the typical position for RR Lyrae stars in Oosterhoff I and Oosterhoff II clusters, respectively (Cacciari et al., 2005; Zorotovic et al., 2010). RRab stars with a value of Dm < 25 are indicated with filled circles, those with a Dm > 25 are indicated with open circles, and the RRab stars for which a good Fourier fit was not obtained are indicated by crosses.
The horizontal branch type of a cluster is another tool that is useful for deter- mining its Oosterhoff classification. The HB type is a measure of the distribution of the stars on the horizontal branch and is defined as HB type= (B − R)/(B + V + R) where B is the number of stars on the horizontal branch that are located blueward of the instability strip, R is the number of stars located redward of the instability strip, and V is the number of variable stars on the horizontal branch. Large values indicate a horizontal branch whose stars trend more toward the blue. I found an HB type of
55 1.8 OoI OoII 1.6 RRab, large Dm RRab, small Dm RRab, no Dm 1.4 RRc RRd
1.2 B A 1
0.8
0.6
0.4
-0.5 -0.45 -0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05
log(Pdays)
Figure 5.10: Bailey diagram, log period vs B-band amplitude, for the RR Lyrae stars in NGC 1466. Symbols are the same as in Figure 5.9
(B − R)/(B + V + R)=0.38 ± 0.05 for NGC 1466. This was determined using the stars in an annulus with an inner radius of 10 arcsec and an outer radius of 75 arcsec; this represented a region for which I felt the sample of the HB stars was complete. This HB type, combined with the metallicity of [Fe/H]≈ −1.60 that was obtained from the RR Lyrae stars, places the cluster outside of the “forbidden region”, where Oo-int objects tend to fall, in the HB type-metallicity diagram (Fig. 7 in Catelan 2009). If one used a lower metallicity similar to what was favored by Walker (1992b) or Olszewski et al. (1991), NGC 1466 would be located much closer to the forbidden region. A lower metallicity would also be consistent with the theoretical predictions by Bono et al. (1994) for Oo-int behavior, whereas the higher metallicity would indi- cate an HB morphology that is too red with respect to the predictions of the models (see Fig. 8 in Catelan 2009). Figures 5.11 and 5.12 show the histograms of both the raw and the fundamental-
56 ized periods, respectively, for the RRab and RRc stars in NGC 1466. RRc periods are fundamentalized by adding 0.128 to the logarithm of their period (van Albada & Baker, 1973); this artificially transforms the RRc stars into RRab stars and allows for a study of the period distribution in a cluster without the effects of the transition from RRab to RRc stars. Catelan (2004a) found that a number of OoI and OoII clusters in the Milky Way have sharply peaked fundamentalized period distributions. In contrast, NGC 1466 shows a broad peak in its fundamentalized period distribution, consistent with it being an Oo-int cluster. The distribution of the raw periods for the RRab stars displays two peaks, a broad one around 0.55 days and a sharper peak at 0.70 days. This is similar to the distribution seen in NGC 1835, an Oo-int cluster, (Soszy´nski et al., 2003) although the shorter period peak for NGC 1466 is broader and its longer period peak occurs at a slightly longer period. Soszy´nski suggested that this two-peaked distribution may be an indicator of a sum of Oo-I and Oo-II characteristics, but the Bailey diagram shows no evidence of an Oo-II population.
14
12
10
8 N
6
4
2
0 0.3 0.4 0.5 0.6 0.7 Period (Days)
Figure 5.11: Distribution of raw periods of the RRab and RRc stars found in NGC 1466.
57 14
12
V08 10 V13 V09 V22 V21 8 V28 V23 N V01 V05 V38 V26 V04 V19 6 V66 V48 V06 V20 V68 V57 V14 V35 V16 4 V03 V02 V15 V50 V30 V10 V07 V39 V55 V46 V25 V24 2 V40 V56 V49 V47 V29 V42 V58 V63 V64 V33 V45 V61 0 0.3 0.4 0.5 0.6 0.7 Period (Days)
Figure 5.12: Distribution of fundamentalized periods of the RRab and RRc stars found in NGC 1466.
Tables 10.1 and 10.2 give the mean physical parameters for RRab and RRc stars, respectively, in a selection of previously studied globular clusters. The parameters that were calculated for NGC 1466 fall between those for Oo-I and Oo-II clusters, consistent with NGC 1466 having an Oo-int classification. A more thorough compar- ison of the physical parameters for the RR Lyrae stars in NGC 1466 and the other globular clusters in this study is carried out in Chapter 10.
58 Chapter 6: Reticulum
Like NGC 1466, Reticulum is an old globular cluster that is located ≈ 11◦ from the center of the LMC (Demers & Kunkel, 1976). It has a metal abundance of [Fe/H] ≈ −1.66 (Mackey & Gilmore, 2004a) and is not very reddened, E(B-V) = 0.016 (Schlegel, 1998). Mackey & Gilmore found that the age of Reticulum is similar to the ages of the oldest globular clusters in the Milky Way and the LMC, having an age that is approximately 1.4 Gyr younger than Milky Way globular cluster M3. Johnson et al. (2002) used Hubble Space Telescope observations to determine that Reticulum formed within 2 Gyr of the other old LMC clusters. Reticulum is a sparsely populated cluster, but it does have a distinct horizontal branch that stretches across the instability strip (Figures 6.1 and 6.2). Twenty-two RR Lyrae stars were first found in the cluster by Demers & Kunkel (1976). Walker (1992a) later found an additional ten RR Lyrae stars, bringing the total in the cluster to 32; 22 RRab stars, 9 RRc’s, and 1 candidate RRd. Ripepi et al. (2004) found RRd behavior in four of the RR Lyrae that had previously been discovered. No new RR Lyrae stars are expected to be found in the central regions of Reticulum since this area is uncrowded and blending is not an issue. I obtained 82 V , 72 B, and 78 I images which comprise a larger data set than the 33 BV pairs obtained by Walker, allowing me to better sample the light curves of the variable stars. Data reduction and variable identification were carried out as described in Chapter 4. The uncrowded nature of Reticulum was ideal for Daophot’s point spread function
59 photometry and while ISIS was run on the images for completeness, it did not find any additional variable stars. Photometry from Daophot was transformed to the standard system using the Landolt standard fields PG0231, SA95, and SA98. I compared my resulting photometry to four of the local standard stars used by Walker (1992a), finding that for these four stars my photometry was 0.034±0.010 magnitudes brighter in V and 0.040 ± 0.008 in B. I decided not to adjust the photometry due to the relatively small number of local standards from Walker with which to compare.
16 RRab RRc 17 RRd
18
19
V 20
21
22
23
24 -0.5 0 0.5 1 1.5 B-V
Figure 6.1: V ,B − V CMD for Reticulum with the position of the RR Lyrae variables also indicated. Plus symbols indicate RRab stars, filled triangles indicated RRc’s, and circles indicate RRd’s.
60 18 RRab RRc RRd
18.5
V 19
19.5
20 -0.2 0 0.2 0.4 0.6 0.8 B-V
Figure 6.2: V ,B − V CMD for Reticulum that is zoomed in on the horizontal branch. The symbols used are the same as in Figure 6.1
6.1 Variable Stars
A total of 32 RR Lyrae stars were found: 22 RRab stars, 4 RRc’s, 5 RRd’s, and 1 candidate RR Lyrae. The study by Walker (1992a) recovered all of these stars. The 5 RRd stars were originally classified as RRc stars by Walker but the larger number of observations in my data set allowed for the identification of them as double mode RR Lyrae. The variable stars in Reticulum, their classification, and their coordinates are listed in Table 6.1. The RRab and RRc stars and their observed characteristics (periods, V and B amplitudes, intensity-weighted V and B mean magnitudes, and magnitude-weighted mean B − V color) are listed in Table 6.2. The RRd stars, their fundamental and first overtone periods and amplitudes, their period ratios, and their mean magnitudes and color are listed in Table 6.3. Walker identified the variables
61 Figure 6.3: Sample light curve for RRab stars in Reticulum. in his paper using their star number in the catalog compiled in Demers & Kunkel (1976). I introduce a new naming system that features only the variable stars and is ordered based on increasing RA. The names used by Walker are listed in the last column in Tables 6.2 and 6.3. Figures 6.3, 6.4, and 6.5 show example light curves for the RRab, RRc, and RRd stars, respectively; the full set of light curves can be found in Appendix B.
62 Figure 6.4: Sample light curve for RRc stars in Reticulum.
63 0.6 P_0 V 18.4 0.4 18.6 0.2 18.8 0 19 -0.2 19.2 -0.4 19.4 0.6 P_1 B 18.8 0.4 19 0.2 19.2 0 19.4 -0.2 19.6 -0.4 19.8
0 0.5 1 1.5 2 0 0.5 1 1.5 2 Phase Phase
Figure 6.5: Sample light curve for RRd stars in Reticulum.
64 Table 6.1: Variable Stars in Reticulum
ID RA (J2000) DEC (J2000) Type P (days) Other IDs
V01 04:35:51.4 -58:51:03.4 RRab 0.50988 DK92 V02 04:35:56.5 -58:52:32.0 RRab 0.61868 DK7 V03 04:35:58.6 -58:53:06.7 RRd 0.4746 DK41 V04 04:36:00.3 -58:52:50.0 RRd 0.4748 DK4 V05 04:36:04.1 -58:52:29.4 RRab 0.57185 DK80 V06 04:36:05.4 -58:51:48.0 RRab 0.59529 DK97 V07 04:36:05.5 -58:50:51.9 RRab 0.51044 DK117 V08 04:36:05.8 -58:49:35.1 RRab 0.64495 DK135 V09 04:36:05.9 -58:50:24.6 RRab 0.54493 DK137 V10 04:36:06.4 -58:52:12.8 RRc 0.35257 DK77 V11 04:36:06.4 -58:51:48.7 - - DK98 V12 04:36:07.1 -58:50:55.0 RRc 0.29627 DK181 V13 04:36:07.7 -58:51:47.0 RRab 0.60958 DK99 V14 04:36:07.8 -58:51:44.6 RRab 0.58659 DK100 V15 04:36:09.1 -58:52:25.9 RRd 0.4762 DK72 V16 04:36:09.8 -58:52:50.8 RRab 0.52289 DK49 V17 04:36:10.2 -58:53:13.7 RRab 0.51288 DK38 V18 04:36:10.6 -58:49:50.4 RRab 0.56005 DK142 V19 04:36:11.9 -58:49:18.2 RRab 0.48486 DK146 V20 04:36:12.2 -58:51:23.3 RRab 0.56073 DK112 V21 04:36:12.3 -58:49:24.5 RRab 0.60704 DK145 V22 04:36:13.4 -58:52:32.1 RRab 0.51358 DK57 V23 04:36:13.8 -58:51:19.3 RRab 0.46862 DK108 V24 04:36:17.3 -58:51:26.3 RRd 0.4670 DK110
65 Table 6.1 (continued)
ID RA (J2000) DEC (J2000) Type P (days) Other IDs
V25 04:36:17.4 -58:53:02.7 RRc 0.32990 DK36 V26 04:36:18.5 -58:51:52.0 RRab 0.65616 DK67 V27 04:36:18.7 -58:51:44.6 RRab 0.51383 DK64 V28 04:36:19.2 -58:50:15.7 RRc 0.31993 DK151 V29 04:36:20.1 -58:52:33.6 RRab 0.50815 DK37 V30 04:36:20.2 -58:52:47.7 RRab 0.53500 DK35 V31 04:36:24.4 -58:50:40.1 RRab 0.50517 DK25 V32 04:36:31.9 -58:49:53.2 RRd 0.4739 DK157
Table 6.2: Photometric Parameters for Variables in Reticulum, Excluding RRd Stars
ID Type P (days) AV AB hV i hBi hB − V i Other IDs V01 RRab 0.50988 1.24 - 19.051 - - DK92 V02 RRab 0.61868 0.67 0.87 19.076 19.432 0.371 DK7 V05 RRab 0.57185 0.95 1.13 19.059 19.413 0.376 DK80 V06 RRab 0.59529 0.92 1.10 19.064 19.412 0.364 DK97 V07 RRab 0.51044 1.21 1.53 19.026 19.304 0.317 DK117 V08 RRab 0.64495 0.48 0.64 19.080 19.486 0.414 DK135 V09 RRab 0.54493 0.76 0.91 19.011 19.310 0.313 DK137 V10 RRc 0.35257 0.43 0.56 19.056 19.321 0.272 DK77 V11------DK98 V12 RRc 0.29627 0.27 0.30 19.031 19.154 0.124 DK181 V13 RRab 0.60958 0.77 0.91 19.075 19.439 0.378 DK99 V14 RRab 0.58659 0.82 1.01 19.057 19.456 0.421 DK100
66 Table 6.2 (continued)
ID Type P (days) AV AB hV i hBi hB − V i Other IDs V16 RRab 0.52289 1.27 1.50 19.031 19.308 0.325 DK49 V17 RRab 0.51288 0.98 1.12 19.022 19.334 0.348 DK38 V18 RRab 0.56005 1.00 1.30 19.076 19.401 0.354 DK142 V19 RRab 0.48486 1.27 1.62 19.048 19.312 0.315 DK146 V20 RRab 0.56073 1.03 1.36 19.073 19.425 0.371 DK112 V21 RRab 0.60704 0.81 0.97 19.074 19.433 0.376 DK145 V22 RRab 0.51358 0.98 1.24 19.033 19.329 0.323 DK57 V23 RRab 0.46862 1.27 1.54 19.053 19.312 0.297 DK108 V25 RRc 0.32990 0.55 0.69 19.017 19.238 0.231 DK36 V26 RRab 0.65616 0.35 0.53 19.076 19.474 0.407 DK67 V27 RRab 0.51383 1.28 1.53 19.023 19.347 0.369 DK64 V28 RRc 0.31993 0.53 0.65 18.987 19.201 0.224 DK151 V29 RRab 0.50815 1.22 1.44 19.026 19.350 0.350 DK37 V30 RRab 0.53500 1.27 1.53 18.987 19.300 0.343 DK35 V31 RRab 0.50517 1.17 1.59 19.069 19.328 0.317 DK25
Table 6.3: Photometric Parameters for the RRd Variables in Reticulum
ID Type P0 (d) P1 (d) P1/P0 AV,0 AV,1 AB,0 AB,1 hV i hBi hB − V i V03 RRd 0.4746 0.3538 0.7455 0.18 0.42 0.21 0.51 19.010 19.306 0.295 V04 RRd 0.4748 0.3532 0.7439 0.07 0.45 0.11 0.53 19.067 19.337 0.277 V15 RRd 0.4762 0.3541 0.7435 0.30 0.35 0.42 0.42 19.139 19.425 0.288 V24 RRd 0.4670 0.3476 0.7443 0.27 0.40 0.31 0.49 19.054 19.327 0.282 V32 RRd 0.4739 0.3523 0.7434 0.08 0.41 0.12 0.53 19.033 19.302 0.277
67 The RRab stars have intensity-weighted mean magnitudes of hV i = 19.05 ± 0.01 and hBi = 19.38 ± 0.01 while the RRc stars have mean magnitudes of hV i = 19.02 ± 0.01 and hBi = 19.23 ± 0.04. The results for RRab stars are brighter than the mean magnitudes of hV i = 19.08 ± 0.01 and hBi = 19.41 ± 0.02 found by Walker. My values for the RRc stars are also slightly brighter than Walker’s mean magnitudes of hV i = 19.05±0.02 and hBi = 19.28±0.04. These differences in brightness for the RR Lyrae stars are on the same order as, and are likely due to, the previously mentioned slight photometric disagreement between my results and those of Walker. In general my periods agreed with those of Walker to within 0.0002 days. V08 and V19 were the only stars for which a difference in period greater than 0.01 days was found. V08 showed an increase in period of 0.012 days in my data while V19 showed a decrease of 0.016 days. These differences in period could be due to either an error in period determination in the previous studies or due to actual period changes. Period changes in RR Lyrae stars can be used to study the evolution of these stars as they move through the instability strip (Catelan, 2009a). A decrease in period indicates a blueward movement on the HR diagram while an increase in period indicates a redward move. In addition to period changes due to evolution, RR Lyrae stars are also known to undergo irregular period changes, of which the exact cause is not known. The size of these period changes is larger than expected for evolutionary period change and larger than seen in other RR Lyrae, and are thus most likely due to an error in period determination by Walker. The first overtone periods for the RRd stars show good agreement with the periods that Walker had reported. Three of the five RRd stars (V03, V15, V24) were also found by Ripepi et al. (2004). The candidate RR Lyrae, V11, was classified as an RRd star by Ripepi et al. (2004) and in my data it displays RRd like behavior but I was unable to determine a reliable period. Figure 6.6 shows the Petersen diagram
68 for the RRd stars in Reticulum along with those in the field of the LMC, similar to Figure 5.6. The RRd stars for Reticulum fall in the same region of the diagram as Milky Way Oo-I clusters tend to fall (Clementini et al., 2004).
0.75 Field Reticulum
0.748
0.746
0.744 P1/P0
0.742
0.74
0.738 0.42 0.44 0.46 0.48 0.5 0.52 0.54 0.56 0.58 0.6 Fundamental Period (days)
Figure 6.6: Petersen diagram showing the ratio of the first overtone period to the fun- damental mode period vs. fundamental mode period for the RRd stars in Reticulum (blue triangles). Also plotted are the RRd stars in the LMC field (red plus symbols) from Soszy´nski et al. (2003).
6.2 Physical Properties of the RR Lyrae Stars
RR Lyrae physical properties were determined using the equations in Sections 4.3.2 and 4.3.3. A Fourier decomposition was performed for 12 RRab and 3 RRc light curves. Tables 6.4 and 6.5 give the Fourier coefficients for the RRab and RRc stars, respectively. The physical properties determined from these coefficients are given in Tables 6.6 and 6.7.
69 Table 6.4: Fourier Coefficients for RRab Variables
ID A1 A21 A31 A41 φ21 φ31 φ41 Dmax Order V02 0.246 0.435 0.2746 0.1546 2.5163 5.1796±0.0881 1.8363 10.34 7 V06 0.328 0.459 0.362 0.232 2.356 4.941±0.092 1.525 1.93 10 V07 0.404 0.437 0.359 0.219 2.277 4.692±0.097 1.023 46.09 9 V13 0.278 0.437 0.331 0.171 2.364 5.121±0.078 1.640 3.89 9 V14 0.301 0.388 0.300 0.185 2.473 5.068±0.103 1.490 48.47 9 V16 0.443 0.416 0.329 0.231 2.386 4.918±0.074 1.288 41.67 11 V18 0.351 0.462 0.349 0.221 2.221 4.852±0.088 1.320 45.79 10 V20 0.363 0.457 0.353 0.226 2.311 4.756±0.086 1.085 44.65 8 V21 0.281 0.499 0.326 0.195 2.311 5.126±0.088 1.623 2.97 7 V27 0.432 0.447 0.347 0.207 2.164 4.599±0.062 0.980 38.92 9 V30 0.439 0.372 0.293 0.212 2.368 4.817±0.110 1.309 50.98 8 V31 0.389 0.454 0.370 0.212 2.109 4.668±0.086 1.004 47.03 10
Table 6.5: Fourier Coefficients for RRc Variables
ID A1 A21 A31 A41 φ21 φ31 φ41 Order V10 0.221 0.165 0.0602 0.066 4.789 3.712±0.491 2.227 8 V25 0.277 0.171 0.0967 0.043 4.551 2.873±0.174 1.118 6 V28 0.274 0.176 0.071 0.041 4.578 2.762±0.216 1.640 8
The mean metallicity of the RRab stars is [Fe/H]J95 = −1.48 ± 0.03 which on the
Zinn & West scale is [Fe/H]ZW84 = −1.65±0.02. This value is in good agreement with the metallicity of [Fe/H]≃ −1.66 found by Mackey & Gilmore (2004a). On the other
70 hand, the relation from Morgan, Wahl, & Wieckhorst (2007) gives a metallicity for
the RRc stars of [Fe/H]ZW84 = −1.80 ± 0.05, which is significantly more metal-poor than the values obtained from the RRab stars and the literature. While this difference in metallicity could be caused by errors in the Fourier analysis, the fact that the other physical properties obtained for the RRc stars are consistent with expectations lends support to the validity of the obtained Fourier coefficients.
Table 6.6: Derived Physical Properties for RRab Variables
hV −Ki hB−V i hV −Ii ID [Fe/H]J95 hMV i hV − Ki log Teff hB − V i log Teff log Teff V02 -1.409 0.773 1.197 3.800 0.363 3.803 3.802 V06 -1.603 0.742 1.182 3.803 0.350 3.806 3.807 V07 -1.481 0.799 1.082 3.814 0.321 3.818 3.812 V13 -1.439 0.765 1.179 3.803 0.359 3.804 3.804 V14 -1.386 0.781 1.147 3.806 0.348 3.808 3.807 V16 -1.244 0.786 1.050 3.816 0.311 3.822 3.819 V18 -1.534 0.771 1.140 3.807 0.338 3.811 3.810 V20 -1.666 0.755 1.145 3.807 0.336 3.811 3.811 V21 -1.418 0.768 1.172 3.803 0.358 3.805 3.804 V27 -1.625 0.771 1.098 3.812 0.314 3.819 3.819 V30 -1.446 0.761 1.092 3.812 0.309 3.821 3.820 V31 -1.484 0.811 1.084 3.813 0.324 3.817 3.816
Mean -1.478 0.774 1.131 3.808 0.336 3.812 3.811 σ 0.034 0.005 0.014 0.002 0.006 0.002 0.002
71 Table 6.7: Derived Physical Properties for RRc Variables
ID [Fe/H]ZW84 hMV i M/M⊙ log(L/L⊙) log Teff Y V10 -1.701 0.646 0.558 1.724 3.861 0.271 V25 -1.864 0.691 0.666 1.742 3.861 0.261 V28 -1.826 0.702 0.674 1.735 3.862 0.263
Mean -1.797 0.680 0.633 1.734 3.861 0.265 σ 0.049 0.017 0.038 0.005 0.001 0.006
6.3 Distance Modulus
As with NGC 1466, the absolute magnitude-metallicity relationship from Catelan & Cort´es (2008) is used to provide the absolute magnitude of the RR Lyrae stars in Reticulum. The disagreement between the metallicities for RRab and RRc stars raises an issue as to which metallicity to use for calculating the absolute magnitude. Since the metallicity obtained from the RRab stars is consistent with what has been reported in the literature and is drawn from a larger number of stars, that value is used, [Fe/H]ZW84 = −1.65 ± 0.02. This value gives an absolute magnitude of
MV =0.61 ± 0.16. The average magnitude of the RRab stars, hV i = 19.050 ± 0.055, and the reddening value of E(B-V) = 0.016 from Schlegel (1998) are used, along with a standard extinction law of AV /E(B − V )=3.1, to obtain a reddening-corrected distance modulus of (m − M)0 = 18.39 ± 0.17. This distance modulus is the same as the value of 18.39 ± 0.12 found by Ripepi et al. (2004). This is shorter than the distance modulus of (m − M)LMC = 18.44 ± 0.11 that Catelan & Cort´es (2008) derived for the LMC, though the two distance moduli agree within the errors. This is not necessarily a surprise as Reticulum is widely separated from the disk of the
72 LMC, having a location that is about 11 degrees from the center of the LMC (Walker, 1992a).
6.4 Oosterhoff Classification
The average periods for the RR Lyrae stars in Reticulum are hPabi =0.552 days and
hPci = 0.324 days. I found 22 RRab stars, 4 RRc’s, 5 RRd’s, and 1 potential RRd
which gives the cluster a number fraction of Nc+d/Nc+d+ab = 0.31. The average periods for the RRab and RRc stars strongly indicate an Oosterhoff I classification and, while the number fraction is high, it is still consistent with the cluster being an
Oo-I object. The minimum period for an RRab star in Reticulum is Pab,min =0.46862 days, which is also consistent with an Oo-I classification for Reticulum (Section 9.2).
1.4 OoI OoII RRab 1.2 RRc RRd
1
V 0.8 A
0.6
0.4
0.2 -0.55 -0.5 -0.45 -0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1
log(Pdays)
Figure 6.7: Bailey diagram, log period vs V -band amplitude for the RR Lyrae stars in Reticulum. Red and green lines indicate the typical position for RR Lyrae stars in Oosterhoff I and Oosterhoff II clusters, respectively (Cacciari et al., 2005; Zorotovic et al., 2010).
73 OoI 1.6 OoII RRab RRc 1.4 RRd
1.2
B 1 A
0.8
0.6
0.4
-0.55 -0.5 -0.45 -0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1
log(Pdays)
Figure 6.8: Same as Figure 6.7 except with B-band amplitudes in place of the V -band amplitudes.
Figures 6.7 and 6.8 show the V and B band period-amplitude diagrams for Retic- ulum. Both diagrams show that the RRab stars cluster along the line that indicates the typical location for RRab stars in Oo-I clusters. There is more scatter in the positions of the RRc stars but most of them still are located near the Oo-I locus, confirming the classification of Reticulum as an Oo-I object.
74 Chapter 7: NGC 1786
Unlike the previous clusters discussed in Chapters 5 and 6, NGC 1786 is located near the center of the LMC. Mucciarelli et al. (2009) found a metallicity of [Fe/H] = −1.75 ± 0.01 from high-resolution spectroscopy of seven red giant stars. However, Olszewski et al. (1991) found a slightly lower value of −1.87 ± 0.20 from the low- resolution spectra of two giant stars; these values are consistent within the error bars. Sharma et al. (2010) reported that NGC 1786 is not very reddened, having an E(B-V) =0.06, and has an age of 12.3 Gyr. This age is consistent with Johnson et al. (2002) finding that NGC 1786 formed within 2 Gyr of the other old LMC clusters through the comparison of the cluster CMD with theoretical isochrones. NGC 1786 is a fairly centrally concentrated cluster which, combined with its location near the center of the LMC, makes it difficult to get accurate photometry of the stars in the center due to blending. Graham (1985) was the first to find variable stars in NGC 1786. Graham found 12 variables, for which he determined periods of 10. Walker & Nemec (1988) later observed NGC 1786 and confirmed the variable nature of 11 of Graham’s stars, though Walker was also only able to determine periods for ten of the stars. Of the variables with known periods, 4 were classified as RRab stars, 5 as RRc stars, and one as a likely Anomalous Cepheid. More recently the Optical Gravitational Lensing Experiment-III (OGLE-III) ob- served the central portion of the LMC and many of its associated globular clusters, including NGC 1786 (Udalski et al., 2008). The OGLE-III survey is designed to find
75 instances of gravitational lensing by looking for small changes in the brightness of stars in its field of view; a natural consequence of this project is the discovery and monitoring of variable stars. OGLE-III greatly increased the number of identified variable stars in NGC 1786. A total of 55 RR Lyrae stars within the tidal radius were reported by Soszy´nski et al. (2009): 28 RRab, 18 RRc, and 9 RRd stars. The location of NGC 1786 near the center of the LMC means that some of these RR Lyrae stars likely belong to the field population of the LMC and not to the cluster. Data reduction and variable identification was carried out in the same way as the other clusters in my study. Photometry was converted to the standard system using standard stars from Stetson (2000) which were located within the field of NGC 1786. Of the 25 Stetson standard stars that appeared in my observations, the average difference between my photometry and that of Stetson is 0.002±0.008 mags in V and 0.002 ± 0.011 mags in B. The extremely crowded nature of NGC 1786 meant that ISIS had to be used extensively to locate variable stars in the center of the cluster.
7.1 Variable Stars
I found 65 variable stars within the my 5.2×5.2 arcminute field of view in the direction of NGC 1786. This includes the cluster as well as the surrounding area. The variables include 36 RR Lyraes (15 RRab, 17 RRc, and 4 RRd), 15 candidate RR Lyraes, 3 classical Cepheids, 1 Type II Cepheid, 1 Anomalous Cepheid, 2 eclipsing binaries, 2 Delta Scuti variables, and 5 variables of undetermined type. The extreme crowding in the central region of NGC 1786 posed some difficulties for the identification and classification of the variable stars due to many of the stars being blended with near neighbors. Table 7.1 lists the variable stars in NGC 1786, their coordinates, and their classification while Table 7.2 lists the photometric properties for all of the variables with the exception of the RRd stars which are listed in Table 7.3. Variable stars V01 through V11 were originally found by Graham (1985) and have periods confirmed by
76 Walker & Nemec (1988). The names for these stars are the same as the ones used by Graham and Walker. NGC 1786’s location toward the center of the LMC means that a significant amount of contamination from LMC field stars is expected in the images. This makes it difficult to determine with absolute certainty whether an individual variable star is a member of the cluster. NGC 1786 has a tidal radius of 2 arcminutes (Bica et al., 2008) and 60 of the 65 variable stars are located within that tidal radius. The 5 stars (2 RRab stars, 1 RRc, 1 classical Cepheid, and 1 eclipsing binary) outside the tidal radius are not cluster members and they are noted in Table 7.1 with the word ’Field’ after their name. The field of view in the images obtained with SOAR is 5.2 × 5.2 arcminutes, thus approximately half of the image is contained within the tidal radius of NGC 1786. The LMC field should feature a roughly even distribution of variable stars, thus the majority of the 60 variables found within the tidal radius should be members of the cluster. Classical Cepheids are younger stars, thus the two classical Cepheids that are within the tidal radius of NGC 1786 should be members of the LMC field. The amount of LMC field star contamination is still significant within the tidal radius of the cluster, as can be seen in Figures 7.1 and 7.2, where the presence of the field stars makes it difficult to distinguish a horizontal branch in the CMD for NGC 1786. The scatter in the position of the RR Lyrae stars in the CMD is likely due to the crowded nature of the central region of the cluster which results in many of the RR Lyrae being partially blended with nearby stars, affecting their brightness and color.
Table 7.1: Variable Stars in NGC 1786
ID RA(J2000) DEC(J2000) Type P (days) Ogle-III ID
V01 04:58:51.3 -67:44:23.7 AC 0.80006 ACEP-009 V02 04:58:52.623 -67:43:53.75 RRd 0.4906 RRLYR-02626
77 Table 7.1 (continued)
ID RA(J2000) DEC(J2000) Type P (days) Ogle-III ID
V03 04:59:00.4 -67:44:40.3 RRab 0.62195 RRLYR-02661 V04 04:59:01.1 -67:43:29.4 RRab 0.55583 RRLYR-02662 V05 04:59:02.8 -67:46:06.0 RRab 0.69706 RRLYR-02674 V06 04:59:07.9 -67:45:29.4 ? 0.30420 RRLYR-02712 V07 04:59:08.9 -67:44:08.0 RRc 0.29536 RRLYR-02727 V08 04:59:12.0 -67:43:52.6 RRab 0.57169 RRLYR-02748 V09 04:59:12.5 -67:44:15.0 RRc 0.36347 RRLYR-02757 V10 04:59:14.1 -67:44:23.7 RRab 0.69652 RRLYR-02770 V11 04:59:14.8 -67:44:21.3 RRc 0.31536 RRLYR-02777 V13 04:59:08.9 -67:44:39.6 RR? 0.55944 V14 04:59:03.1 -67:44:39.1 RRc 0.31786 RRLYR-02676 V15 04:59:09.4 -67:44:39.0 RR? 0.42735 RRLYR-02732 V16 04:59:06.0 -67:44:39.6 RR? 0.35429 RRLYR-02693 V17 04:59:06.3 -67:44:38.3 RR? 0.52470 RRLYR-02697 V18 04:59:11.4 -67:44:36.3 RRab 0.64515 RRLYR-02747 V19 04:59:04.2 -67:44:35.6 RRab 0.74479 RRLYR-02680 V20 04:59:09.4 -67:44:34.4 ? 0.29193 V21 04:58:59.309 -67:44:32.06 RRd 0.4920 RRLYR-02653 V22 04:59:10.1 -67:44:27.2 RRc 0.32920 RRLYR-02738 V23 04:59:04.8 -67:44:24.9 RR? 0.52851 RRLYR-02683 V24 04:59:11.2 -67:44:17.4 RR? 0.41110 RRLYR-02743/02746 V25-Field 04:59:41.3 -67:44:16.8 Ceph 3.27005 CEP-0591 V26 04:59:09.2 -67:44:14.3 RRab 0.73891 RRLYR-02729 V27 04:59:14.5 -67:43:52.2 RRab 0.66428 RRLYR-02776 V28 04:58:59.684 -67:43:52.12 RRd 0.4854 RRLYR-02658
78 Table 7.1 (continued)
ID RA(J2000) DEC(J2000) Type P (days) Ogle-III ID
V29 04:59:14.1 -67:43:46.2 RRc 0.36944 RRLYR-02771 V30 04:59:07.2 -67:43:30.9 Ceph 11.71808 CEP-0561 V31 04:59:06.6 -67:43:26.2 Eclipse 0.61/1.6 V32-Field 04:59:34.7 -67:42:46.7 RRab 0.53199 RRLYR-02855 V33-Field 04:59:28.9 -67:42:40.1 RRab 0.53278 RRLYR-02834 V34-Field 04:58:59.3 -67:42:38.3 Eclipse 1.6/3.2 V35-Field 04:59:36.0 -67:42:31.9 RRc 0.33059 RRLYR-02864 V36 04:59:39.4 -67:42:15.1 DeltaScuti 0.07723 DSCT-400 V37 04:59:09.0 -67:46:14.9 RRc 0.35528 RRLYR-02728 V38 04:59:21.2 -67:46:06.7 RRab 0.75890 RRLYR-02802 V39 04:59:03.0 -67:45:36.2 DeltaScuti 0.08040 V40 04:58:59.6 -67:45:24.6 RRc 0.33496 RRLYR-02657 V41 04:59:06.1 -67:45:24.4 T2Ceph 1.10416 T2CEP-020 V42 04:59:01.4 -67:45:21.5 RRc 0.37066 RRLYR-02667 V43 04:58:49.9 -67:45:10.7 ? 0.06096 V44 04:59:15.6 -67:45:02.9 RRc 0.36458 RRLYR-02781 V45 04:59:08.8 -67:45:01.9 RRc 0.29913 RRLYR-02724 V46 04:59:09.2 -67:45:01.6 Ceph 2.16504 CEP-0563 V47 04:59:06.2 -67:44:56.3 RR? 0.37080 RRLYR-02698 V48 04:59:12.197 -67:44:56.28 RRd 0.4786 RRLYR-02750 V49 04:59:05.7 -67:44:55.9 ? 0.55403 V50 04:59:10.0 -67:44:55.6 RRab 0.49336 RRLYR-02737 V51 04:59:03.0 -67:44:54.1 RR? 0.56363 RRLYR-02675 V52 04:59:09.3 -67:44:53.4 RRc 0.32653 RRLYR-02730 V53 04:59:05.6 -67:44:52.8 RR? 0.36824 RRLYR-02688
79 Table 7.1 (continued)
ID RA(J2000) DEC(J2000) Type P (days) Ogle-III ID
V54 04:59:05.0 -67:44:51.8 RRc 0.30898 RRLYR-02686 V55 04:59:08.9 -67:44:51.7 RRab 0.51904 RRLYR-02725 V56 04:59:04.0 -67:44:50.7 RR? 0.52757 RRLYR-02678 V57 04:59:09.5 -67:44:50.5 RR? 0.52083 RRLYR-02733 V58 04:59:04.9 -67:44:49.1 RRab 0.55049 RRLYR-02685 V59 04:59:07.3 -67:44:48.7 RR? 0.56507 RRLYR-02706 V60 04:59:11.6 -67:44:46.8 RRc 0.29205 V61 04:59:12.0 -67:44:43.9 RRc 0.36061 RRLYR-02749 V62 04:59:05.9 -67:44:43.3 RRc 0.36411 RRLYR-02692 V63 04:59:07.9 -67:44:48.6 RR? 0.62312 RRLYR-02714 V64 04:59:07.8 -67:44:52.6 RR? 0.70228 RRLYR-02711 V65 04:59:06.6 -67:44:42.0 RR? 0.64660 RRLYR-02702 V66 04:59:07.5 -67:44:35.7 RR? 0.50999 RRLYR-02671
Table 7.2: Photometric Parameters for Variables in NGC 1786, Excluding RRd Stars
ID Type P (days) AV AB hV i hBi hB − V i V01 AC 0.80006 0.61 0.71 17.774 18.133 0.367 V03 RRab 0.62195 0.91 1.17 19.457 19.959 0.526 V04 RRab 0.55583 1.10 1.35 19.218 19.560 0.377 V05 RRab 0.69706 0.61 0.82 19.301 19.730 0.441 V06 ? 0.30420 0.64 0.89 20.539 20.924 0.402 V07 RRc 0.29536 0.56 0.75 19.292 19.603 0.325 V08 RRab 0.57169 0.86 1.17 19.220 19.661 0.463
80 Table 7.2 (continued)
ID Type P (days) AV AB hV i hBi hB − V i V09 RRc 0.36347 0.47 0.56 19.445 19.571 0.132 V10 RRab 0.69652 0.69 0.79 19.474 19.962 0.494 V11 RRc 0.31536 0.54 0.63 19.339 19.608 0.275 V13 RR? 0.55944 0.36 0.68 17.761 18.500 0.746 V14 RRc 0.31786 0.62 0.77 19.473 19.806 0.345 V15 RR? 0.42735 - - - - - V16 RR? 0.35429 - - - - - V17 RR? 0.52470 0.33 0.68 17.855 18.693 0.852 V18 RRab 0.64515 0.97 1.20 19.083 19.491 0.439 V19 RRab 0.74479 0.43 0.57 18.807 19.322 0.522 V20 ? 0.29193 - 0.43 - 19.215 - V22 RRc 0.32920 0.63 0.72 19.330 19.564 0.243 V23 RR? 0.52851 0.50 0.93 18.383 19.030 0.672 V24 RR? 0.41110 0.30 0.39 18.682 18.955 0.275 V25-Field Ceph 3.27005 0.84 1.16 15.694 16.258 0.601 V26 RRab 0.73891 0.39 0.48 19.179 19.630 0.455 V27 RRab 0.66428 0.58 0.60 18.990 19.234 0.245 V29 RRc 0.36944 0.26 0.38 19.083 19.523 0.444 V30 Ceph 11.71808 1.11 1.75 14.324 14.799 0.607 V31 Eclipse 0.61/1.6 - - 18.340 18.376 0.036 V32-Field RRab 0.53199 1.11 1.46 19.089 19.384 0.322 V33-Field RRab 0.53278 0.67 0.71 19.587 20.028 0.430 V34-Field Eclipse 1.6/3.2 - - 19.514 19.754 0.240 V35-Field RRc 0.33059 0.49 0.60 19.186 19.551 0.371 V36 DeltaScuti 0.07723 0.56 0.62 20.319 20.485 0.172
81 Table 7.2 (continued)
ID Type P (days) AV AB hV i hBi hB − V i V37 RRc 0.35528 0.47 0.59 19.355 19.590 0.241 V38 RRab 0.75890 0.40 0.47 19.014 19.438 0.427 V39 DeltaScuti 0.08040 0.28 0.41 20.699 21.044 0.349 V40 RRc 0.33496 0.55 0.66 19.631 20.026 0.403 V41 T2Ceph 1.10416 1.01 1.26 18.462 18.746 0.328 V42 RRc 0.37066 0.47 0.54 19.307 19.633 0.329 V43 ? 0.06096 0.70 0.84 21.365 21.636 0.283 V44 RRc 0.36458 0.48 0.58 19.297 19.648 0.356 V45 RRc 0.29913 0.68 0.71 19.389 19.560 0.180 V46 Ceph 2.16504 0.30 0.41 15.829 16.328 0.504 V47 RR? 0.37080 0.75 1.00 19.977 20.444 0.491 V49 ? 0.55403 0.20 0.24 17.294 18.223 0.929 V50 RRab 0.49336 0.74 0.88 18.601 18.866 0.263 V51 RR? 0.56363 0.40 0.58 18.335 18.898 0.574 V52 RRc 0.32653 0.47 0.57 18.989 19.317 0.333 V53 RR? 0.36824 - - - - - V54 RRc 0.30898 0.41 0.48 19.332 19.669 0.339 V55 RRab 0.51904 0.97 1.14 18.720 18.860 0.154 V56 RR? 0.52757 0.44 0.67 19.736 20.036 0.318 V57 RR? 0.52083 - - - - - V58 RRab 0.55049 0.63 0.71218.821 19.185 0.371 V59 RR? 0.56507 - - - - - V60 RRc 0.29205 0.32 0.42 19.217 19.502 0.289 V61 RRc 0.36061 0.48 0.60 19.274 19.900 0.624 V62 RRc 0.36411 0.28 0.44 18.969 19.512 0.550
82 Table 7.2 (continued)
ID Type P (days) AV AB hV i hBi hB − V i V63 RR? 0.62312 - - - - - V64 RR? 0.70228 - - - - - V65 RR? 0.64660 - - - - - V66 RR? 0.50999 - - - - -
Table 7.3: Photometric Parameters for the RRd Variables in NGC 1786
ID Type P0 (d) P1 (d) P1/P0 AV,0 AV,1 AB,0 AB,1 hV i hBi hB − V i V02 RRd 0.4906 0.3647 0.7434 0.12 0.19 0.10 0.25 19.144 19.442 0.306 V21 RRd 0.4920 0.3664 0.7448 0.08 0.23 0.11 0.29 19.443 19.806 0.367 V28 RRd 0.4854 0.3605 0.7427 0.14 0.22 0.16 0.31 19.200 19.493 0.308 V48 RRd 0.4786 0.3555 0.7427 0.32 0.32 0.43 0.42 19.324 19.729 0.409
7.1.1 RR Lyrae Stars
A total of 13 RRab, 16 RRc, 4 RRd, and 15 candidate RR Lyrae stars were found within the tidal radius of NGC 1786; 1 RRc and 1 candidate RR Lyrae are new discoveries that have not been found in any of the previous studies of the cluster. All of the 9 RR Lyrae stars originally identified by Graham (1985) were found. V2 had been classified as an RRc star by Graham (1985) and Walker & Nemec (1988). However, the larger number of epochs in my data set allowed for the detection of a second pulsation mode in this star and it has been reclassified as an RRd star. These nine stars have intensity-weighted mean magnitudes of hV i = 19.321 ± 0.039 and
83 16 RRab RRc RRd 17
18
19 V 20
21
22
23 -0.5 0 0.5 1 1.5 B-V
Figure 7.1: V ,B − V CMD for stars within the tidal radius of NGC 1786 with the positions of the RR Lyrae variables also indicated. Plus symbols indicate RRab stars, filled triangles indicate RRc’s, and circles indicate RRd’s. The contamination by LMC field stars is readily apparent. The scatter in the positions of the RR Lyrae stars is a consequence of blending that arises from the crowded nature of the central region of the cluster. hBi = 19.677 ± 0.059. These are fainter than Walker’s values (hV i = 19.203 ± 0.073 and hBi = 19.526 ± 0.066). This disagreement in brightness is potentially due to the improved resolution of my observations decreasing the effect of blending between the RR Lyrae stars and other nearby stars. Sample light curves for the RR Lyrae stars in NGC 1786 are shown in Figures 7.3-7.5, the full set of light curves can be found in Appendix C. Soszy´nski et al. (2009) found 55 RR Lyrae stars within the tidal radius of NGC 1786 using the OGLE-III data. I found 49 of these stars in my data, the remaining six are located within the extremely crowded core of the cluster. Of the OGLE-III
84 18 RRab RRc RRd
18.5
V 19
19.5
20 -0.2 0 0.2 0.4 0.6 0.8 B-V
Figure 7.2: V ,B − V CMD for NGC 1786 that is zoomed in on the horizontal branch. The symbols used are the same as in Figure 7.1 stars that were found in my data set, 32 were classified as RR Lyrae stars (13 RRab, 15 RRc, and 4 RRd), 16 as candidate RR Lyrae, and 1 as a variable of undetermined type. V06 (OGLE-III RRLYR-02712) was classified as an RRab star by Soszy´nski et al. (2009), however I found it to have an intensity-weighted mean magnitude of hV i = 20.539, about one magnitude fainter than the horizontal branch. Sosy´nski found a mean magnitude of hV i = 19.410 for this star, about one magnitude brighter than my value. Since V06 is not in a very crowded region of the cluster, the reason for this disagreement in brightness is unknown. OGLE-III stars RRLYR-02743 and RRLYR-07246 are only slightly separated on the sky (≈ 0.15 arcseconds) and can potentially be a single star. My photometry only found one variable star at this location, V24, which has an RR Lyrae-like shape and
85 Figure 7.3: Sample light curve for RRab stars in NGC 1786. period but is brighter than the horizontal branch, likely due to blending with nearby non-variable neighbors, and thus has been listed as a candidate RR Lyrae. The candidate RR Lyrae stars are all located toward the center of the cluster. ISIS was used to find 9 of the candidate RR Lyrae stars (V15, V16, V53, V57, V59, V63-V66); the location of these stars in the extremely crowded center of the cluster did not allow Daophot light curves to be obtained. Of the remaining candidate RR Lyrae stars, V17, V23, and V51 are more than one magnitude brighter than the horizontal branch and have colors that are redder than the confirmed RR Lyrae stars, possibly due to blending. V47 is approximately 0.5 magnitudes fainter than the horizontal branch and shows potential RRd behavior but a second period could not be determined. V56 has a large gap in its light curve which potentially impacts
86 Figure 7.4: Sample light curve for RRc stars in NGC 1786. the accuracy of the determination of its period and amplitude.
7.2 Physical Properties of the RR Lyrae Stars
Physical properties for 7 RRab and 7 RRc stars were calculated using the Fourier decomposition of their light curves, as described in Chapter 4. One of the RRc stars, V35, is located outside of the tidal radius of NGC 1786 and is thus a member of the LMC field. Tables 7.4 and 7.5 list the Fourier coefficients for the RRab and RRc stars, respectively, while Tables 7.6 and 7.7 list the physical properties of these stars. The averages of the physical properties for the RRc stars are calculated using only the 6 stars that are within the tidal radius of the cluster.
87 0.6 18.5 P_0 V 0.4
0.2 19
0
-0.2 19.5 -0.4
0.6 P_1 B 0.4 19
0.2
0 19.5 -0.2
-0.4 20
0 0.5 1 1.5 2 0 0.5 1 1.5 2 Phase Phase
Figure 7.5: Sample light curve for RRd stars in NGC 1786.
88 Table 7.4: Fourier Coefficients for RRab Variables
ID A1 A21 A31 A41 φ21 φ31 φ41 Dmax Order V03 0.369 0.446 0.249 0.178 2.47 5.03±0.18 1.25 46.35 6 V04 0.454 0.396 0.232 0.090 2.30 4.93±0.10 1.09 26.97 10 V05 0.229 0.397 0.318 0.122 2.26 5.54±0.17 2.34 12.15 7 V08 0.308 0.492 0.320 0.107 2.13 4.75±0.27 1.20 5.65 7 V10 0.235 0.564 0.300 0.173 2.39 4.97±0.30 1.76 6.73 7 V26 0.175 0.377 0.153 0.076 2.46 5.88±0.36 2.27 39.77 8 V38 0.161 0.336 0.192 0.102 2.96 6.05±0.32 2.32 8.42 7
Table 7.5: Fourier Coefficients for RRc Variables
ID A1 A21 A31 A41 φ21 φ31 φ41 Order V07 0.274 0.284 0.121 0.079 4.44 2.23±0.36 1.22 8 V11 0.276 0.202 0.109 0.051 4.70 2.67±0.43 1.58 6 V37 0.231 0.109 0.073 0.026 4.40 2.35±0.82 5.90 6 V44 0.246 0.171 0.088 0.054 4.93 3.66±0.43 3.02 8 V45 0.285 0.303 0.103 0.060 3.94 2.17±1.11 1.15 8 V62 0.128 0.223 0.122 0.042 3.49 2.19±0.50 1.11 7 V35-Field 0.242 0.066 0.062 0.035 5.31 4.17±0.46 2.64 7
89 Table 7.6: Derived Physical Properties for RRab Variables
hV −Ki hB−V i hV −Ii ID [Fe/H]J95 hMV i hV − Ki log Teff hB − V i log Teff log Teff V03 -1.625 0.695 1.166 3.805 0.332 3.811 3.812 V04 -1.399 0.737 1.073 3.814 0.301 3.824 3.822 V05 -1.346 0.709 1.247 3.795 0.380 3.797 3.796 V08 -1.741 0.764 1.184 3.803 0.347 3.807 3.808 V10 -2.106 0.649 1.342 3.787 0.377 3.793 3.798 V26 -1.120 0.711 1.232 3.796 0.388 3.795 3.793 V38 -0.994 0.708 1.223 3.796 0.396 3.794 3.790
Mean -1.476 0.710 1.210 3.800 0.3602 3.803 3.803 σ 0.144 0.134 0.031 0.001 0.013 0.004 0.004
Table 7.7: Derived Physical Properties for RRc Variables
ID [Fe/H]ZW84 hMV i M/M⊙ log(L/L⊙) log Teff Y V07 -1.804 0.685 0.739 1.730 3.864 0.261 V11 -1.819 0.689 0.685 1.734 3.862 0.263 V37 -2.112 0.700 0.790 1.806 3.853 0.240 V44 -1.820 0.634 0.575 1.742 3.859 0.266 V45 -1.850 0.725 0.755 1.738 3.863 0.259 V62 -2.139 0.733 0.833 1.827 3.851 0.234 V35-Field -1.197 0.672 0.480 1.668 3.868 0.292
Mean -1.924 0.694 0.699 1.763 3.859 0.259 σ 0.064 0.014 0.047 0.017 0.002 0.007
90 The mean metallicity for the RRab stars is [Fe/H]J95 = −1.48 ± 0.14 which in the Zinn & West scale is [Fe/H]ZW84 = −1.65 ± 0.10. This is more metal-rich than the literature values, see introduction to this chapter, though it is consistent within the error bars. The mean metallicity found for the RRc stars is [Fe/H]ZW84 = −1.92 ± 0.06, which is more metal-poor than any of the literature values. The LMC field RRc star, V35, in Table 7.7 immediately stands out by being much more metal- rich than any of the other RRc stars.
7.3 Distance Modulus
The absolute magnitude-metallicity relationship from Catelan & Cort´es (2008) is used to find the absolute magnitude of the RR Lyrae stars in NGC 1786. Since the metallicity obtained for the RRab stars, [Fe/H]ZW84 = −1.65 ± 0.10, is closer to the metallicities reported in the literature, it is used for this calculation, giving a V
absolute magnitude of hMV i =0.605± 0.216. Using the mean observed V magnitude for the RRab stars, hV i = 19.090 ± 0.079, the reddening value given by Sharma et
al. (2010), E(B-V) = 0.06, and a standard extinction law with AV /E(B − V )=3.1
gives a reddening-corrected distance modulus of (m − M)0 = 18.30 ± 0.23. This is
shorter than the distance modulus of (m − M)LMC = 18.44 ± 0.11 that Catelan & Cort´es (2008) derived for the LMC. The location of NGC 1786 is near the center of the LMC, and the cluster distance modulus is expected to be similar to that of the LMC. In order to determine if the discrepancies between these two values are a result of blending, the distance modulus is recalculated using on the six RRab stars within the cluster radius that do not have any nearby neighbors that could cause blending (V03, V04, V05, V10, V26, and V27). The average observed V magnitude for these six stars is hV i = 19.270 ± 0.075 which changes the distance modulus to
(m − M)0 = 18.48 ± 0.23. This new value agrees with the distance modulus found by Catelan & Cort´es (2008), indicating that the distance modulus using the full set
91 of RRab stars was effected by blending.
7.4 Oosterhoff Classification
The average periods for the RR Lyrae stars in NGC 1786 are hPabi =0.626 days and hPci = 0.335 days. The division between Oosterhoff intermediate and Oosterhoff II clusters occurs at an average RRab period of 0.62 days; the average RRab period for NGC 1786 is just on the Oo-II side of this division. In contrast, the average period for the RRc stars suggests an Oosterhoff I classification. I found 13 RRab, 16 RRc, and 4 RRd stars in NGC 1786 which gives the cluster a Nc+d/Nc+d+ab =0.606. This ratio suggests an Oo-II classification, though it is a higher ratio than is typically seen.
The minimum RRab period in the cluster is Pab,min =0.49336 days which is on the shorter period end of what is seen for Oo-II objects (Section 9.2). Figures 7.6 and 7.7 show the V and B band period-amplitude diagrams for NGC 1786. Both diagrams show a great deal of scatter in the location of both the RRab and RRc stars. The RRc stars tend to be located closer to the Oo-I locus which would be consistent with the average RRc period. Figure 7.8 shows the Petersen diagram which includes the RRd stars in NGC 1786 as well as those in the LMC field. The RRd stars in NGC 1786 fall in the same region as RRd stars in Milky Way Oo-I objects. The Oosterhoff classification of NGC 1786 is more complicated than that of the other clusters observed for this dissertation. The first overtone dominant pulsators, the RRc and RRd stars, suggest an Oo-I classification for the cluster. However the fundamental mode pulsators, the RRab stars, suggest an Oo-II classification. The picture is further complicated by the fact that some of the RR Lyrae within the tidal radius are likely LMC field stars and should not be included when looking at the behavior of the cluster RR Lyrae stars.
92 1.4 OoI OoII RRab 1.2 RRc RRd
1
V 0.8 A
0.6
0.4
0.2 -0.55 -0.5 -0.45 -0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1
log(Pdays)
Figure 7.6: Bailey diagram, log period vs V -band amplitude (for the RR Lyrae stars in NGC 1786. Red and green lines indicate the typical position for RR Lyrae stars in Oosterhoff I and Oosterhoff II clusters, respectively (Cacciari et al., 2005; Zorotovic et al., 2010).
93 OoI 1.6 OoII RRab RRc 1.4 RRd
1.2
B 1 A
0.8
0.6
0.4
-0.55 -0.5 -0.45 -0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1
log(Pdays)
Figure 7.7: Same as Figure 7.6 except with B-band amplitudes in place of the V -band amplitudes.
94 0.75 LMC Field NGC 1786
0.748
0.746
0.744 P1/P0
0.742
0.74
0.738 0.42 0.44 0.46 0.48 0.5 0.52 0.54 0.56 0.58 0.6 Fundamental Period (days)
Figure 7.8: Petersen diagram showing the ratio of the first overtone period to the fundamental mode period vs. fundamental mode period for the RRd stars in NGC 1786 (blue triangles). Also plotted are the RRd stars in the LMC field (red plus symbols) from Soszy´nski et al. (2003).
95 Chapter 8: NGC 2210
NGC 2210 is the fourth and final LMC cluster investigated as part of this dissertation. NGC 2210 is located closer to the center of the LMC than either NGC 1466 or Reticulum but is farther from the center than NGC 1786, and thus does not suffer from the effects of LMC field contamination to the same extent as NGC 1786 does. Mucciarelli et al. (2010) found a metallicity for the cluster of [Fe/H] = −1.65 ± 0.02 from spectral observations of 5 red giant stars. Olszewski et al. (1991) found a more metal poor value of [Fe/H] = −1.97 ± 0.20 based on the spectra of 4 stars in the cluster. The cluster is not very reddened, having an E(B-V)= 0.075 (Schlegel, 1998). Graham (1977) and Nemec (1981) were the first to search NGC 2210 and the surrounding area for variable stars. Walker (1985) found 9 RR Lyrae stars in the cluster. The number of known RR Lyrae stars grew thanks to work done by Hazen & Nemec (1992) which found 33 variables, including 11 RR Lyrae, in the cluster as well as 52 field RR Lyrae in the nearby vicinity. Reid & Freedman (1994) observed a 15 × 15 arcminute area around NGC 2210, finding 44 variable stars (at least 27 were RR Lyraes). Like NGC 1786, NGC 2210 was observed by the OGLE survey which found 58 RR Lyrae stars in the direction of the cluster (Soszy´nski et al., 2009). I obtained a total of 109 V , 106 B, and 106 I images on the SOAR and SMARTS telescopes. I reduced the data as described in Chapter 4 and the photometry was transformed to the standard system using observation of the Landolt standard fields PG0231, PG0942, PG1047, SA95, and SA98 (Landolt, 1992). I had combined the
96 data sets from the two telescopes and was in the process of identifying and classifying the variable stars in NGC 2210 when I became aware that similar work on the cluster was being carried out by another group of investigators (Young-Beom Jeon, James Nemec, and Alistair Walker). This group had obtained 270 B and V images using the CTIO 0.9-m telescope. Considering the size of the two data sets, it was decided that it would be best to collaborate on this cluster, with Young-Beom Jeon handling the process of combining my photometry with theirs.
8.1 RR Lyrae Stars
The work of combining the data sets and identifying the variable stars is primarily being carried out by Young-Beom Jeon and is still underway. Currently 49 RR Lyrae stars (32 RRab, 16 RRc, and 1 RRd) have been identified. Table 8.1 lists the identified RR Lyrae stars, their classification, period, and V and B-band amplitudes.
Table 8.1: Photometric Parameters for Variables in NGC 2210
ID Type P (days) AV AB hV i hBi hB − V i v767 RRc 0.306089 0.49 0.70 19.089 19.259 0.170 v861 RRab 0.535503 1.05 1.36 19.163 19.449 0.286 v873 RRc 0.369854 0.42 0.51 18.658 18.956 0.298 v900 RRab 0.66241 1.13 1.52 18.924 19.264 0.340 v909 RRc 0.398029 0.51 0.67 19.252 19.528 0.276 v920 RRab 0.6565 0.89 1.13 19.038 19.411 0.373 v938 RRab 0.64005 1.05 1.30 19.009 19.368 0.359 v942 RRab 0.52391 1.21 1.62 19.106 19.407 0.301 v974 RRab 0.60238 1.11 1.38 19.137 19.46 0.323 v980 RRc 0.357005 0.38 0.49 19.008 19.233 0.225 v998 RRc 0.310231 0.44 0.54 19.162 19.353 0.191
97 Table 8.1 (continued)
ID Type P (days) AV AB hV i hBi hB − V i v1020 RRc 0.397151 0.52 0.64 19.029 19.299 0.270 v1087 RRab 0.722514 0.59 0.75 19.073 19.461 0.388 v1109 RRab 0.733037 0.49 0.61 19.116 19.513 0.397 v1127 RRab 0.684187 0.74 0.94 19.016 19.33 0.314 v1143 RRab 0.627733 1.09 1.41 19.068 19.395 0.327 v1204 RRab 0.562166 1.22 1.57 19.184 19.48 0.296 v1206 RRc 0.383952 0.47 0.61 19.092 19.335 0.243 v1217 RRab 0.623082 0.94 1.15 19.134 19.475 0.341 v1233 RRab 0.705148 0.55 0.73 19.106 19.485 0.379 v1252 RRc 0.270223 0.34 0.43 19.371 19.543 0.172 v1296 RRc 0.358951 0.55 0.71 19.200 19.461 0.261 v1301 RRd 0.3552 0.69 0.88 19.093 19.325 0.232 v1349 RRc 0.282076 0.56 0.70 19.259 19.46 0.201 v1372 RRc 0.285777 0.34 0.43 19.238 19.426 0.188 v1385 RRc 0.435544 0.48 0.61 19.118 19.387 0.269 v1411 RRab 0.523234 1.08 1.37 19.222 19.49 0.268 v1452 RRab 0.608591 0.42 0.56 19.505 19.931 0.426 v1465 RRab 0.610946 1.07 1.38 19.278 19.585 0.307 v1484 RRab 0.583317 0.92 1.20 19.240 19.584 0.344 v1560 RRab 0.63577 0.81 1.07 19.273 19.651 0.378 v1584 RRab 0.512013 1.23 1.59 19.170 19.45 0.280 v2110 RRab 0.617179 0.55 0.71 19.413 19.796 0.383 v2404 RRab 0.436395 0.99 1.28 19.713 20.093 0.380 v16940 RRab 0.60227 0.87 1.10 19.275 19.596 0.321 v17861 RRc 0.376606 0.45 0.56 19.144 19.46 0.316
98 8.2 Physical Properties of the RR Lyrae Stars
Prior to deciding to combine data sets with the other group, I had performed Fourier fits on 4 RRab and 4 RRc stars that I had identified from my data. The Fourier coefficients from these fits are given in Tables 8.2 and 8.3 for the RRab and RRc stars, respectively. The physical properties obtained are given in Tables 8.4 and 8.5. The RRab star v2404 has a metallicity that is nearly one dex higher than any of the other three RRab stars. This combined with the star’s location away from the center of the cluster make it likely that it is an LMC field star, not a cluster member, and thus it is not included in the calculation of the mean values for the physical properties.
Table 8.2: Fourier Coefficients for RRab Variables
ID A1 A21 A31 A41 φ21 φ31 φ41 Dmax Order v942 0.438 0.415 0.350 0.233 2.198 4.562±0.0484 0.849 44.35 10 v1109 0.199 0.394 0.215 0.102 2.561 5.641±0.092 2.483 15.67 9 v1143 0.383 0.467 0.340 0.213 2.396 5.154±0.053 1.636 2.24 8 v2404 0.316 0.517 0.333 0.192 2.382 5.109±0.071 1.582 1.56 9
Table 8.3: Fourier Coefficients for RRc Variables
ID A1 A21 A31 A41 φ21 φ31 φ41 Order v980 0.179 0.122 0.088 0.025 4.79 3.11±0.20 1.83 6 v998 0.220 0.135 0.018 0.028 4.79 3.20±0.92 0.81 7 v1296 0.233 0.142 0.053 0.012 4.63 3.47±0.32 2.64 8 v1372 0.161 0.120 0.011 0.040 4.41 0.66±1.47 3.23 5 99 Table 8.4: Derived Physical Properties for RRab Variables
hV −Ki hB−V i hV −Ii ID [Fe/H]J95 hMV i hV − Ki log Teff hB − V i log Teff log Teff v942 -1.728 0.751 1.109 3.811 0.315 3.818 3.819 v1109 -1.405 0.684 1.286 3.791 0.385 3.795 3.795 v1143 -1.492 0.693 1.165 3.804 0.340 3.810 3.809 v2404 -0.521 0.987 0.950 3.825 0.324 3.825 3.816
Mean -1.542 0.709 1.187 3.802 0.347 3.807 3.808 σ 0.097 0.021 0.052 0.006 0.020 0.007 0.007
Table 8.5: Derived Physical Properties for RRc Variables
ID [Fe/H]ZW84 hMV i M/M⊙ log(L/L⊙) log Teff Y v980 -1.965 0.688 0.653 1.764 3.857 0.256 v998 -1.542 0.725 0.594 1.696 3.866 0.277 v1296 -1.857 0.696 0.599 1.746 3.859 0.263 v1372 -1.973 0.764 1.082 1.806 3.857 0.232
Mean -1.834 0.718 0.732 1.753 3.860 0.257 σ 0.101 0.017 0.117 0.023 0.002 0.009
The mean metallicity of the RRab stars is [Fe/H]J95 = −1.54 ± 0.10, which in the
Zinn & West scale is [Fe/H]ZW84 = −1.69 ± 0.07. This value is consistent with the value of [Fe/H] = −1.65 ± 0.02 found by Mucciarelli et al. (2010). As was seen in Reticulum and NGC 1786, the Morgan, Wahl, & Wieckhorst (2007) calibration gives
100 a lower metallicity for the RRc stars, [Fe/H]ZW84 = −1.83 ± 0.10.
8.3 Distance Modulus
The absolute magnitude-metallicity relation from Catelan & Cort´es (2008) and the metallicity from the RRab stars was used to obtain an absolute magnitude of MV = 0.60 ± 0.21 The average magnitude for the RRab stars is 19.189 ± 0.038 and the reddening is E(B-V)= 0.075 (Schlegel, 1998). These values, along with a standard extinction law with AV /E(B − V )=3.1, gives a reddening-corrected distance mod-
ulus of (m − M)0 = 18.36 ± 0.21. This is shorter than the distance modulus of
(m − M)LMC = 18.44 ± 0.11 that Catelan & Cort´es (2008) derived for the LMC, though it is consistent within the errors.
8.4 Oosterhoff Classification
The average periods for the RR Lyrae stars in NGC 2210 are hPabi = 0.612 days
and hPci = 0.350 days. With a total of 32 RRab, 16 RRc, and 1 RRd, NGC 2210
has a Nc+d/Nc+d+ab = 0.35. All three of these values are indicative of an Oo-int classification for the cluster. The minimum period for the RRab stars in the cluster
is Pab,min =0.51049 days which supports an Oo-int classification (Section 9.2). Figures 8.1 and 8.2 show the V and B-band Bailey diagrams for the cluster. The RRab stars in the diagrams have a large scatter with a significant portion of them being located between the Oo-I and II loci, consistent an Oo-int classification, though there is a significant number that cluster along the Oo-II locus. The RRc stars also show a significant amount of scatter with a large portion of them falling between the Oo-I and II lines.
101 1.4 OoI OoII RRab 1.2 RRc RRd
1
V 0.8 A
0.6
0.4
0.2 -0.5 -0.4 -0.3 -0.2 -0.1
log(Pdays)
Figure 8.1: Bailey diagram, log period vs V -band amplitude for the RR Lyrae stars in NGC 2210. Red and green lines indicate the typical position for RR Lyrae stars in Oosterhoff I and Oosterhoff II clusters, respectively (Cacciari et al., 2005; Zorotovic et al., 2010).
102 OoI 1.6 OoII RRab RRc 1.4 RRd
1.2
B 1 A
0.8
0.6
0.4
-0.5 -0.4 -0.3 -0.2 -0.1
log(Pdays)
Figure 8.2: Same as Figure 8.1 except with B-band amplitudes in place of the V -band amplitudes.
103 Chapter 9: Exploring Oosterhoff Intermediate Systems
As discussed in Chapter 3, the fact that Oosterhoff intermediate stellar systems are not seen in the Milky Way, but are prevalent in the nearby dwarf galaxies and their globular clusters, presents a challenge to the hierarchical model for Milky Way forma- tion. Since Oo-int stellar systems do not occur in the Milky Way, they have not been studied to the same extent as Oo-I/II stellar systems, which occur at closer distances and thus have been easier to observe. In fact, the greater distances involved mean that extragalactic Oo-I/II stellar systems have not been studied as well as their Milky Way counterparts. I undertook this study in an attempt to compare extragalactic Oo-I/II stellar systems to their Galactic counterparts, as well as study the differences between the RR Lyrae stars in Oo-int systems and those in Oo-I/II systems.
9.1 Structure of the Instability Strip
RR Lyrae variable stars inhabit a region of the horizontal branch where the instability strip intersects it (see Figure 3.1). The effective temperatures of stars determine the red and blue edges of the instability strip. The blue edge of the instability strip marks where stars become too hot, pushing their ionization zones outward to the point where they are too close to the surface for pulsations to occur. The red edge marks the point where stars become too cool and convection takes over as the primary
104 method of energy transport in the outer layers of the star. In addition to the instability strip having defined edges, there is an internal struc- ture to the position of different classes of RR Lyrae stars within the instability strip. RRab stars tend to be located to the red side of the instability strip while the RRc stars are located on the blue side. This is illustrated in Figure 9.1 and can also be seen clearly in Figure 5.2 which shows the horizontal branch of NGC 1466. The RRd stars also tend to be on the blue side of the instability strip, though they do not appear as far blue as some RRc stars, which is consistent with the first overtone being the dominant pulsation mode in most RRd stars.
Figure 9.1: Depiction of the structure of the instability strip theorized by van Albada & Baker (1973). The blue (left) end of the instability strip is populated by RRc stars while RRab stars populate the red (right) end. The center of the instability strip is a “hysteresis zone” (labeled with an H) where the pulsation mode depends on the direction of evolution. Evolution toward the blue (left pointing arrow) produces mainly RRab stars in the hysteresis zone, as in an Oo-I cluster, while redward evo- lution produces primarily RRc stars in this zone, as in an Oo-II cluster. Figure from Smith (1995)
As can be seen in Figure 5.2, the transition between the RRab and RRc stars within the instability strip is not sudden, instead there is a region in the middle of
105 the strip which contains both fundamental mode and first overtone pulsators. Van Albada & Baker (1973) theorized that the central part of the instability strip is a “hysteresis zone”, into which the RR Lyrae stars in this zone have evolved from elsewhere in the instability strip and their mode of pulsation is set by where they started out. Thus RRc stars in the hysteresis zone originally started out further to the blue and have evolved redward while RRab stars in this region are evolving toward the blue from initial positions that are on the red side of the hysteresis zone. The period/temperature which marks the transition point between RRab and RRc stars is not constant. Instead this transition point, which can be represented through the period of the RRab star with the shortest period in a cluster, Pab,min, is an indicator of Oosterhoff status. The transition between RRab and RRc stars occurs at shorter periods, and thus higher temperatures, in Oosterhoff I objects (Catelan et al. 2011, in preparation). Van Albada & Baker (1973) explain this connection between the transition period and the Oosterhoff type of the cluster as being due to the hysteresis zone and the general direction of horizontal branch evolution in the cluster. In this explanation the RR Lyrae stars in Oo-I objects are primarily evolving from red to blue, meaning that more RRab stars are moving into the hysteresis zone, pushing the transition between RRab and RRc stars more toward the blue and shorter periods. In Oo-II objects the evolution is occuring from blue to red, populating the hysteresis zone with more RRc stars and thus pushing the transition toward the red and longer periods (Fig. 9.1). Stellingwerf (1975) and Stellingwerf & Bono (1993) made similar predictions regarding the hysteresis zone.
9.2 Indicators of Oosterhoff Status
Catelan et al. 2011 (in prep) are currently working on examining how well Pab,min, as well as other properties, serve as indicators of Oosterhoff type. As part of this effort I helped to compile and analyze an updated list of the properties of RR Lyrae
106 Figure 9.2: Average period of RRab stars vs Pab,min for globular clusters with at least 5 known RRab stars. Large symbols indicate clusters with more than 10 RRab stars while small symbols indicate clusters with less that 10 RRab stars. The dashed lines define the region occupied by the majority of the globular clusters. The hatched area is the region occupied by the majority of the Oo-int clusters. stars in all globular clusters known to have at least 5 RRab stars. This list includes a total of 65 Galactic and Local Group globular clusters; 27 are Oo-I, 22 Oo-II, and 14 are Oo-int. The properties that were examined include the number of RRab, RRc, and RRd stars, the number fraction of first overtone dominant pulsators, the mean periods for the RRab and RRc stars, the minimum period for an RRab star (Pab,min), and the maximum RRc period in the cluster (Pc,max). The average RRab period is the strongest indicator of Oosterhoff status, in fact the Oosterhoff gap, and thus Oo-int objects, are defined as having an average RRab period that falls in the range of 0.58 ≤ hPabi ≤ 0.62 days (Catelan, 2004b). The other properties were plotted against hPabi in an attempt to see if there were any
107 correlations, especially ones that pertained to Oosterhoff status.
Figure 9.3: Correlation between hPabi and hPci for globular clusters with at least 5 known RRab stars.
Figure 9.2 shows the correlation between hPabi and Pab,min. There is a clear trend between the two properties that includes both Oo-I and Oo-II clusters, with clusters that have a large hPabi also having a large value for Pab,min. While there is range of
Pab,min values at a given hPabi, there is very little overlap in Pab,min values between Oo-I and Oo-II clusters. Oo-int objects fall on the same trend, forming a smooth transition between the Oo-I and Oo-II clusters. This suggests that Oo-int clusters form a link between the other two Oosterhoff groups.
The property that shows the next strongest correlation with hPabi, and thus Oost-
erhoff type, is the average period for RRc stars, hPci. As can be seen in Figure 9.3, there is a general correlation between these two properties, with clusters that have
longer hPabi also having longer hPci. Despite this trend, and in contrast to traditional
108 Figure 9.4: Correlation between hPabi and the number fraction of RRc stars for globular clusters with at least 5 known RRab stars. views (Smith, 1995), hPci does not serve as a good indicator of Oosterhoff status due to the large range in hPci values that overlap for the different Oosterhoff groups.
The number fraction of RRc stars, (Nc)/(Nab + Nc), and Pc,max also do not serve as good indicators of Oosterhoff type. Figures 9.4 and 9.5 show that there is considerable scatter in the relationship between both of these quantities and hPabi. There is also almost complete overlap between the Oosterhoff groups with respect to
Pc,max and the number fraction.
109 Figure 9.5: Correlation between hPabi and Pc,max for globular clusters with at least 5 known RRab stars.
9.3 Bailey Diagrams for Oosterhoff Intermedi- ate Objects
One question that can be asked about Oosterhoff intermediate objects is whether these objects are a mixture of Oo-I and Oo-II stars or whether they represent a population of RR Lyrae that fall in between the two Oosterhoff groups. One can answer this question by looking at the Bailey (period-amplitude) diagrams of Oo-int objects. If these objects are actually a mix of stars with Oo-I and Oo-II properties, one would expect to see significant populations of RR Lyrae stars near both the Oo-I and Oo-II loci on the diagram. Figure 9.6 shows the Bailey diagram for Canes Venatici I (CVn I), a nearby dwarf spheroidal galaxy. CVn I is an Oo-int object and instead of showing signs of a mix of Oo-I and Oo-II stars, the majority of its RRab stars fall between the
110 1.4 OoI OoII RRab 1.2 RRc
1
V 0.8 A
0.6
0.4
0.2 -0.55 -0.5 -0.45 -0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1
log(Pdays)
Figure 9.6: Bailey diagram, log period vs V -band amplitude for the RR Lyrae stars in the dwarf galaxy Canes Venatici I. Data from Kuehn et al. (2008).
Oo-I and Oo-II loci (Kuehn et al., 2008). The Bailey diagram for NGC 1466 (Figure 9.7) supports the case that Oo-int objects are not a mix of Oo-I and Oo-II stars as the RRab stars fall along a line that has a slightly longer period than the Oo-I locus; there is no sign of a significant population of stars with Oo-II properties. Previous work such as van Albada & Baker (1973) and Sandage et al. (1981) have compared the Bailey diagram behavior of clusters of differing Oosterhoff types. This work led to the realization that the Oosterhoff effect exists on a star-by-star basis, with RR Lyrae stars in Oo-II stellar systems being systematically shifted to longer periods at a given amplitude. In the subsections below I carry out a similar analysis, comparing the Bailey diagrams of several Oo-int systems. Table 9.1 lists the metallicity, average periods for the RRab and RRc stars, Pab,min, Pc,max, and the number fraction of first overtone dominant pulsators (fcd) for the stellar systems that are examined.
111 OoI 1.4 OoII RRab, large Dm RRab, small Dm RRab, no Dm 1.2 RRc RRd
1 V A 0.8
0.6
0.4
0.2 -0.5 -0.45 -0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05
log(Pdays)
Figure 9.7: Bailey diagram, log period vs V -band amplitude for the RR Lyrae stars in NGC 1466.
Table 9.1: Properties of Stellar Systems Examined in Section 9.3
Object [Fe/H] HB Type hPabi hPci Pab,min Pc,max fcd
NGC 1466 -1.64 0.38 0.591 0.335 0.4934 0.3770 0.39 NGC 2210 -1.65 0.65 0.612 0.350 0.5105 0.4355 0.35
Draco -2.1 0.615 0.375 0.5366 0.4310 0.21 NGC 2257 -1.95 0.46 0.611 0.333 0.5042 0.3823 0.50 M3 -1.55 0.18 0.555 0.340 0.4560 0.4860 0.21
M15 -2.26 0.67 0.644 0.370 0.5527 0.4406 0.58
112 9.3.1 NGC 1466 vs Draco
The fact that not all Oo-int objects are alike is reinforced when one compares my re- sults for the globular cluster NGC 1466 and the results for the Draco dwarf spheroidal galaxy obtained by Kinemuchi et al. (2008). Draco is more metal poor, [Fe/H]= −2.1, and has a longer average RRab period, hPabi = 0.615 days, than NGC 1466. How- ever, if we compare the Bailey diagrams of these two clusters (Figure 9.8) we see that their RRab stars occupy similar positions on the diagram and show a similar level of scatter. The shortest period RRab star in NGC 1466 has a much shorter period, Pab,min,1466 = 0.4934 days, than the shortest period RRab star in Draco,
Pab,min,Draco = 0.5366 days; since Draco contains more RR Lyrae stars than NGC 1466, this is unlikely to be due to statistical effects.
1.4 OoI OoII NGC 1466 1.2 Draco
1
V 0.8 A
0.6
0.4
0.2 -0.5 -0.45 -0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1
log(Pdays)
Figure 9.8: Bailey diagram, log period vs V -band amplitude, for the RR Lyrae stars in NGC 1466 (blue circles) and Draco (purple triangles).
In contrast to the RRab stars, the majority of RRc stars in NGC 1466 have shorter
113 periods than those in Draco. Combined with the shorter Pab,min, this suggests that the transition between RRc and RRab stars occurs at a shorter fundamental mode period in NGC 1466 than in Draco.
RRd Stars in NGC 1466 and Draco 0.75 LMC Field NGC 1466 Draco 0.748
0.746 P1/P0 0.744
0.742
0.74 0.42 0.44 0.46 0.48 0.5 0.52 0.54 0.56 0.58 0.6 Fundamental Period (days)
Figure 9.9: Petersen diagram showing the ratio of the first overtone period to the fundamental mode period vs. fundamental mode period for the RRd stars in NGC 1466 (blue triangles) and Draco (green circles). Also plotted are the RRd stars in the LMC field (red plus symbols) from Soszy´nski et al. (2003)
The RRd stars in both objects show different Oosterhoff natures. Figure 9.9 shows the RRd stars for both NGC 1466 and Draco plotted on a Petersen diagram. All but one of the RRd stars in Draco have longer fundamental mode periods and higher period ratios than their counterparts in NGC 1466. The RRd stars in Draco occupy a similar position to what is typically seen in Oo-II clusters while those in NGC 1466 enjoy a position similar to those in Oo-I objects (Popielski et al., 2000). Despite their status as Oo-int stellar systems, neither NGC 1466 or Draco have RRd stars that occupy an intermediate position between Oo-I/II clusters.
114 9.3.2 NGC 1466 vs NGC 2210
While Draco and NGC 1466 have a significant difference in metallicity, NGC 1466 and NGC 2210 present an opportunity to compare two Oosterhoff intermediate objects that have nearly equivalent metallicities, [Fe/H] ≈ −1.65. The average RRab period
for NGC 2210 is hPab,2210i = 0.612 days, similar to Draco and longer than the average period of NGC 1466, hPab,1466i = 0.591 days. As was the case with Draco,
NGC 1466 has a shorter minimum RRab period, Pab,min,1466 = 0.4934 days, than
NGC 2210, Pab,min,2210 = 0.51049 days. If one compares the Bailey diagrams for the two clusters (Fig. 9.10), one sees very different behaviors. Both clusters show a great deal of scatter among their RRab stars, with most of those stars falling between the Oo-I and Oo-II loci. NGC 1466 has a group of RRab stars that cluster around the Oo-I locus while NGC 2210 shows essentially the opposite behavior, having a group of RRab stars that cluster around the Oo-II line. The difference in positions of the RRab stars between these two clusters looks very similar to systematic shift in RRab position found by Sandage et al. (1981) when comparing the Galactic globular clusters M3 (Oo-I) and M15 (Oo-II). The strong difference in RRab period-amplitude behavior between NGC 1466 and NGC 2210, despite their similarity in metallicity, indicates that metallicity is not the dominant factor in determining the position of RRab stars on the Bailey diagram, at least not within Oo-int clusters. NGC 1466 has a horizontal branch type of (B − R)/(B + V + R)=0.38 which is redder than the HB type of 0.65 of NGC 2210 (Mackey & Gilmore, 2004b). Figure 8 in Catelan (2009a) plots the relationship between metallicity and HB type; both clusters would fall within the Oo-int region on this figure, however NGC 1466 is located close to the red edge of the Oo-int region while NGC 2210 is located close to the blue edge. If NGC 1466 had a horizontal branch that was slightly redder it would fall in the Oo-I region while if the HB of NGC 2210 was slightly bluer it would fall in the Oo-II region. This suggests that the
115 1.4 OoI OoII NGC 1466 1.2 NGC 2210
1
V 0.8 A
0.6
0.4
0.2 -0.5 -0.45 -0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1
log(Pdays)
Figure 9.10: Bailey diagram, log period vs V -band amplitude, for the RR Lyrae stars in NGC 1466 (blue circles) and NGC 2210 (black triangles). difference in RRab period-amplitude behavior between these two clusters is related to the morphology of their horizontal branches.
9.3.3 NGC 2210 vs NGC 2257
NGC 2257 is another Oosterhoff intermediate globular cluster located in the LMC. It is more metal-poor than NGC 1466 and NGC 2210 with a metallicity of [Fe/H] =
−1.95±0.02 dex (Mucciarelli et al., 2010). NGC 2257 has a hPabi =0.611 days, similar to NGC 2210, and a Pab,min = 0.5042 days (Nemec et al., 2009), which is slightly shorter than in NGC 2210. The combined Bailey diagram for the two clusters (Fig. 9.11) shows that the RRab stars in the two clusters occupy similar positions. The RRab stars exhibit a large amount of scatter, with many being located between the
116 Oo-I and Oo-II loci; however, there is clustering, especially among the low-amplitude RRab stars, near the Oo-II locus. The comparison between NGC 2210 and NGC 2257 is similar to the one involving NGC 1466 and Draco in that both Oo-int stellar systems with different metallicities show similar behavior of their RRab stars on the Bailey diagram.
1.4 OoI OoII NGC 2257 1.2 NGC 2210
1
V 0.8 A
0.6
0.4
0.2 -0.5 -0.45 -0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1
log(Pdays)
Figure 9.11: Bailey diagram, log period vs V -band amplitude, for the RR Lyrae stars in NGC 2210 (black triangles) and NGC 2257 (blue circles). Data for NGC 2257 from Nemec et al. (2009).
Even though the RRab stars in NGC 2257 fall closer to the Oo-II locus, the 3 RRd stars in the cluster all fall in the region of the Petersen diagram that is typically occuppied by RRd stars in Milky Way Oo-I globular clusters (see Figure 20 in Nemec et al. (2009)). As mentioned in Section 9.3.1, Draco features RRab stars that fall closer to the Oo-I locus but its RRd stars mostly fall in the region of
117 the Petersen diagram that is typically occupied by Oo-II clusters. These two stellar systems strongly indicate that in Oosterhoff intermediate objects, the behavior of the RRab and RRd stars are unrelated to each other. There is some indication that the behavior of the RRd stars may be related to the behavior of the RRc stars. The RRc stars for Draco fall near the Oo-II locus (Fig. 9.8) while the RRc stars in NGC 2257 fall more toward the Oo-I locus, consistent with the groupings of their RRd stars on the Petersen diagram.
9.3.4 NGC 1466 and NGC 2210 vs Oosterhoff I/II Systems
1.4 OoI OoII NGC 1466 1.2 M3
1
V 0.8 A
0.6
0.4
0.2 -0.5 -0.45 -0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1
log(Pdays)
Figure 9.12: Bailey diagram, log period vs V -band amplitude, for the RR Lyrae stars in NGC 1466 (blue circles) and M3 (purple triangles). Data for M3 is from Cacciari et al. (2005).
Since NGC 1466 and NGC 2210 feature RRab stars that tend toward either the
118 Oo-I or Oo-II loci in the Bailey diagram, it is worth examining how these two clusters compare to bona fide Oo-I/II clusters. Figure 9.12 shows the combined Bailey diagram for the RR Lyrae stars in NGC 1466 and M3, an Oo-I cluster located in the halo of the Milky Way. M3 has a metallicity of [Fe/H] = −1.55 ± 0.13 (Smolinski et al.,
2011), somewhat more metal-rich than NGC 1466. M3’s hPabi = 0.555 days and
Pab,min = 0.4560 days (Cacciari et al., 2005) are both shorter than what is seen in NGC 1466. The RRab stars in the two clusters occupy similar positions. However, the majority of the RRab stars in M3 show tighter clustering around the Oo-I locus than those in NGC 1466. A bigger difference is seen among the RRc stars; the majority of the RRc stars in M3 are tightly clustered around the Oo-I locus while the RRc stars in NGC 1466 occupy positions between the Oo-I and Oo-II loci. The majority of the RRc stars in M3 are shifted toward a shorter period than their counterparts in NGC
1466. This shift in RRc periods, along with M3 having a shorter Pab,min, supports the transition between RRab and RRc stars in M3 occuring at a shorter period than in NGC 1466. NGC 2210 can also be compared to the Milky Way Oo-II globular cluster M15. M15 is very metal-poor, [Fe/H] = −2.26 (Harris, 2010), and has an average RRab period of hPabi = 0.644 days and a minimum RRab period of Pab,min = 0.5527 days (Corwin et al., 2008), both of which are longer than the values for NGC 2210. Figure 9.13 shows the Bailey diagram for these two clusters. The RRab stars in both clusters show a great deal of scatter and largely occupy similar positions. The major difference in the RRab stars between the two clusters is that the RRab stars in NGC 2210 extend to a shorter period than those in M15. If you remove the five NGC 2210 RRab stars that have a log(P ) ≤ −0.25, the distributions of RRab stars in the two clusters would be essentially the same. The shorter period RRab to RRc transition in NGC 2210 seems to be responsible for the Oo-int classification of the cluster. When compared to bona fide Oo-I/II clusters, the RRab stars in NGC 1466 and
119 1.4 OoI OoII M15 1.2 NGC 2210
1
V 0.8 A
0.6
0.4
0.2 -0.5 -0.45 -0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1
log(Pdays)
Figure 9.13: Bailey diagram, log period vs V -band amplitude, for the RR Lyrae stars in NGC 2210 (black triangles) and M15 (blue circles). Data for M15 is from Corwin et al. (2008).
NGC 2210 seem to occupy similar positions in the Bailey diagram to the RRab stars in the comparison cluster. While the Oo-int clusters show slightly more scatter in the position of their RRab stars, the factor that seems to drive the Oosterhoff classification of these clusters is the transition period between RRab and RRc stars, as indicated by Pab,min.
9.3.5 Oosterhoff Intermediate Locus?
As can been seen in the numerous Bailey diagrams that have been presented in this dissertation, Oo-I and Oo-II objects have loci that mark the typical positions of the RRab stars in these types of clusters. One question that this dissertation hoped to
120 answer pertained to whether a similar locus existed for the RRab stars in Oo-int clusters. A quick look at the Bailey diagram for CVn-I (Fig. 9.6), and the combined Bailey diagrams comparing NGC 1466 to Draco (Fig. 9.8) and to NGC 2210 (Fig. 9.10), shows that such a locus does not exist for Oo-int objects. Despite having a considerable scatter, the RRab stars in NGC 1466 and Draco tend to fall toward the Oo-I locus while the RRab stars in NGC 2210 and NGC 2257 fall more toward the Oo-II locus. CVn-I displays a middle ground between these two extremes with the majority of its RRab stars falling between the Oo-I and Oo-II loci, showing no clustering near either one. Obviously the Bailey diagram behavior of Oo-int objects is complex and further work is needed in order to understand this behavior. The results in this chapter reveal that Oosterhoff intermediate objects do not constitute a homogeneous and entirely separate class. Instead, Oo-int objects seem to represent a transition between Oo-I and Oo-II objects. Many Oo-int objects look very similar to Oo-I/II objects while CVn-I indicates that at least some Oo-int objects represent more of a middle ground. The difference between Oo-int objects that are similar to Oo-I objects and those that are more similar to Oo-II objects may result from a difference in the luminosity of the RR Lyrae stars in these objects, similar to the explanation for the difference between Oo-I and Oo-II clusters. This difference in luminosity has been explained as possibly arising from a difference in the helium content of the stars (Sandage et al., 1981). Applying this to the case of the Oo-int objects this would mean that RR Lyrae stars in objects that are similar to Oo-II objects, such as NGC 2210, have a higher helium content and a higher luminosity than RR Lyrae stars in Oo-int clusters that are more similar to Oo-I objects, such as NGC 1466. Differences between Oo-int and Oo-I/II objects seem to arise due to differences in the transition period between RRab and RRc stars.
121 Chapter 10: Trends in Physical Properties
The physical properties of RR Lyrae stars obtained through Fourier analysis, as dis- cussed in Chapter 4, provide another way to look at the difference between RR Lyrae stars in various clusters. Tables 10.1 and 10.2 give the average physical properties for the RRab and RRc stars, respectively, in previously studied clusters. The majority of the data for the physical properties comes from L´azaro et al. (2006) and Contreras et al. (2010), with the data on M75 coming from Corwin et al. (2003). The metallicity listed in the tables is the cluster metallicity and comes from Harris (2010).
Table 10.1: Mean Physical Properties Obtained for RRab Stars in Previously Studied Globular Clusters
Cluster Oo Type # Stars [Fe/H] hTeff i hMV i NGC6362 I 14 −0.99 6555 0.86 NGC6171 I 3 −1.02 6619 0.85 NGC1851 I 7 −1.18 6494 0.80 M62 I 39 −1.18 6501 0.83 M5 I 26 −1.29 6465 0.81 NGC6229 I 9 −1.47 6477 0.81 NGC6934 I 24 −1.47 6455 0.81 M3 I 17 −1.50 6438 0.78 NGC4147 I 5 −1.80 6633 0.80
122 Table 10.1 (continued)
Cluster Oo Type # Stars [Fe/H] hTeff i hMV i M75 Int 5 −1.24 6529 0.81 M2 II 9 −1.65 6276 0.71 NGC5286 II 12 −1.69 6266 0.72 M9 II 5 −1.77 6305 0.68 M55 II 5 −1.94 6333 0.67 NGC5466 II 9 −1.98 6328 0.52 M92 II 5 −2.31 6160 0.67 M15 II 11 −2.37 6237 0.67
Table 10.2: Mean Physical Properties Obtained for RRc Stars in Previously Studied Globular Clusters
Cluster Oo Type # Stars [Fe/H] hM/M⊙i hlog(L/L⊙)i hTeff i hYi NGC6362 I 15 −0.99 0.53 1.66 7429 0.29 NGC6171 I 6 −1.02 0.53 1.65 7447 0.29 M62 I 21 −1.18 0.53 1.66 7413 0.29 M5 I 14 −1.29 0.54 1.69 7353 0.28 NGC6229 I 9 −1.47 0.56 1.69 7332 0.28 NGC6934 I 4 −1.47 0.63 1.72 7290 0.27 M3 I 5 −1.50 0.59 1.71 7315 0.27 NGC4147 I 9 −1.80 0.55 1.693 7335 0.28 M75 Int 7 −1.29 0.53 1.67 7399 0.29 M2 II 2 −1.65 0.54 1.74 7215 0.27 NGC5286 II 12 −1.69 0.60 1.72 7276 0.27
123 Table 10.2 (continued)
Cluster Oo Type # Stars [Fe/H] hM/M⊙i hlog(L/L⊙)i hTeff i hYi M9 II 2 −1.77 0.60 1.74 7247 0.27 NGC2298 II 2 −1.92 0.59 1.75 7200 0.26 M55 II 5 −1.94 0.53 1.75 7193 0.27 NGC5466 II 7 −1.98 0.52 1.696 7191 0.25 M68 II 16 −2.23 0.70 1.79 7145 0.25 M92 II 3 −2.31 0.64 1.77 7186 0.26 M15 II 8 −2.37 0.76 1.81 7112 0.24
Figures 10.1-10.5 show the average physical properties for the RR Lyrae stars in these clusters plotted against the cluster metallicity; the error bars that are included are meant to be representative and come from the sources referenced in Contreras et al. (2010). The majority of these plots reveal a linear trend with cluster metallicity. The trend of average mass for RRc stars versus cluster metallicity (Fig. 10.3) has the greatest number of outliers from its roughly linear trend. It is also important to note that the Oo-I and Oo-II objects fall along the same linear trend when we look at most of these physical properties. This agreement suggests that the physical properties responsible for the formation of RR Lyrae stars are the same in Oo-I and Oo-II objects. The one exception occurs when looking at average RRab V -band ab- solute magnitude (MV ) versus cluster metallicity (Fig. 10.5). This physical property displays a trend that is more like a step function. The Oo-I clusters demonstrate a linear relationship where more metal-poor clusters feature RRab stars that have slightly brighter absolute magnitudes than more metal-rich clusters. There are not enough Oo-II clusters to determine if they display a similar variation with cluster metallicity or if they occur at a constant absolute magnitude.
124 7550
7500
7450
7400
7350
7300 Teff (K) 7250
7200
7150
7100 OoI OoII OoInt 7050 -2.4 -2.2 -2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 [Fe/H]
Figure 10.1: The average effective temperature, hTeff i, for RRc stars in previously studied globular clusters vs cluster metallicity.
These previously studied clusters are all located in the Milky Way halo and include only one Oo-int cluster, M75; the other three Oo-int clusters in the Milky Way have not had physical properties derived for their RR Lyrae stars. M75, represented by a gray triangle in Figures 10.1-10.5, follows the same trends as the Oo-I and Oo-II clusters. In Figure 10.5, M75 has an absolute magnitude that is similar to the Oo-I clusters. The work done in this dissertation allows us to see if extragalactic Oo-I/II globular clusters follow the same trend as their Milky Way counterparts. This sample increases the number Oo-int clusters for which physical properties have been calculated, allow- ing for a much better comparison between Oo-int and Oo-I/II clusters.. Tables 10.3 and 10.4 summarize the average physical properties for the clusters discussed in this
125 1.84 OoI 1.82 OoII OoInt 1.8
1.78
1.76
1.74
1.72 log(L/Lsun) 1.7
1.68
1.66
1.64
1.62 -2.4 -2.2 -2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 [Fe/H]
Figure 10.2: Average luminosity (in terms of the luminosity of the Sun), hL/L⊙i, for RRc stars in previously studied globular clusters vs cluster metallicity. thesis.
126 -0.05 OoI OoII OoInt -0.1
-0.15
-0.2 log(M/Msun) -0.25
-0.3
-0.35 -2.4 -2.2 -2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 [Fe/H]
Figure 10.3: Average mass (in terms of the mass of the Sun), hM/M⊙i, for RRc stars in previously studied globular clusters vs cluster metallicity.
127 7000 OoI OoII 6900 OoInt
6800
6700
6600
Teff (K) 6500
6400
6300
6200
6100 -2.4 -2.2 -2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 [Fe/H]
Figure 10.4: The average effective temperature, hTeff i, for RRab stars in previously studied globular clusters vs cluster metallicity.
128 0.9
0.85
0.8
0.75
0.7
v 0.65 M
0.6
0.55
0.5
0.45 OoI OoII OoInt 0.4 -2.4 -2.2 -2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 [Fe/H]
Figure 10.5: The average V -band absolute magnitude, hMV i, for RRab stars in previously studied globular clusters vs cluster metallicity.
129 Table 10.3: Mean Physical Properties Obtained for RRab Stars in Globular Clusters in the LMC
Cluster Oo Type # Stars [Fe/H] hTeff i hMV i NGC1466 Int 13 −1.64 6427 0.78 Reticulum I 12 −1.66 6428 0.77 NGC1786 II? 7 −1.77 6300 0.71 NGC2210 Int 3 −1.65 6341 0.71
Table 10.4: Mean Physical Properties Obtained for RRc Stars in Globular Clusters in the LMC
Cluster Oo Type # Stars [Fe/H] hM/M⊙i hlog(L/L⊙)i hTeff i hYi NGC1466 Int 7 −1.64 0.60 1.71 7244 0.27 Reticulum I 3 −1.66 0.63 1.73 7265 0.27 NGC1786 II? 6 −1.77 0.69 1.76 7221 0.25 NGC2210 Int 4 −1.65 0.71 1.75 7242 0.26
Figures 10.6-10.10 show the relationships between RR Lyrae physical properties and cluster metallicity, this time with the addition of the four LMC clusters discussed in this dissertation. In general the four clusters agree very well with the trends seen in the Milky Way halo clusters. In the plot of RRc luminosity vs cluster metallicity (Fig. 10.7) NGC 1786 and NGC 2210 appear to be slightly brighter than the trend, but are consistent within the error bars. NGC 1786 and NGC 2210 again appear to be outliers when one looks at the relationship between RRc mass and cluster metallicity (Fig. 10.8); NGC 2210 may still be consistent within the error bars but NGC 1786
130 7550
7500
7450
7400
7350
7300 Teff (K) 7250
7200 OoI OoII 7150 OoInt NGC 2210 7100 NGC 1466 Reticulum NGC 1786 7050 -2.4 -2.2 -2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 [Fe/H]
Figure 10.6: The average effective temperature, hTeff i, for RRc stars vs cluster metal- licity. is not. However, the presence of other clusters that do not follow the general trend suggests that the relationship between RRc mass and cluster metallicity may not be as tight as the relationships for the other physical properties. Perhaps the most interesting of these relationships is the one between the V -band absolute magnitude for RRab stars and cluster metallicity. As stated previously, this relationship shows a break between Oo-I and Oo-II clusters. Oo-I clusters show a slight trend toward brighter magnitudes at lower metallicities. Oo-II clusters may show a similar trend, though with a shallower slope. The Oo-int clusters straddle the break; NGC 1466, like M75, falls along the Oo-I trend while NGC 2210 fits with the Oo-II clusters. As discussed in section 5.5, while NGC 1466 is an Oo-Int object, it has some characteristics that appear similar to Oo-I clusters: clustering of some
131 1.84 OoI 1.82 OoII OoInt 1.8 NGC 2210 NGC 1466 Reticulum 1.78 NGC1786 1.76
1.74
1.72 log(L/Lsun) 1.7
1.68
1.66
1.64
1.62 -2.4 -2.2 -2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 [Fe/H]
Figure 10.7: Average luminosity (in terms of the luminosity of the Sun), hL/L⊙i, for RRc stars vs cluster metallicity.
RRab stars around the Oo-I locus on the Bailey diagram and RRd stars that fall in the same region on the Petersen diagram as Galactic Oo-I clusters. Thus it is not necessarily a surprise that NGC 1466 behaves like an Oo-I cluster when looking at the RRab absolute magnitude vs cluster metallicity trend. Likewise, NGC 2210 showed clustering along the Oo-II locus in the Bailey diagram by a portion of its RRab stars, which is consistent with its Oo-II like behavior here. This difference in absolute magnitude is also consistent with the difference in Bailey diagram behaviors of NGC 1466 and NGC 2210 as discussed in Section 9.3.2; the observed difference in the positions of the RRab stars in the two clusters is consistent with NGC 2210 RR Lyrae stars being more luminous than their counterparts in NGC 1466.
132 -0.05 OoI OoII OoInt -0.1 NGC 2210 NGC 1466 Reticulum NGC 1786 -0.15
-0.2 log(M/Msun) -0.25
-0.3
-0.35 -2.4 -2.2 -2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 [Fe/H]
Figure 10.8: Average mass (in terms of the mass of the Sun), hM/M⊙i, for RRc stars vs cluster metallicity.
The fact that the LMC globular clusters follow the same trends of physical prop- erty vs cluster metallicity as Galactic globular clusters indicates that the processes involved in the formation of the RR Lyrae stars are the same in both LMC and Galac- tic globular clusters. Clusters in all three Oosterhoff groups follow the same general trends and there is a smooth transition between Oosterhoff groups, except for the RRab V -band absolute magnitude vs cluster metallicity relationship. The behavior of the Oo-int clusters supports the idea that they represent a transition between Oo-I and Oo-II objects as opposed to a separate, homogenous class.
133 7000 OoI OoII 6900 OoInt NGC 2210 6800 NGC 1466 Reticulum NGC 1786 6700
6600
Teff (K) 6500
6400
6300
6200
6100 -2.4 -2.2 -2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 [Fe/H]
Figure 10.9: The average effective temperature, hTeff i, for RRab stars vs cluster metallicity.
134 0.9
0.85
0.8
0.75
0.7
v 0.65 M
0.6
0.55 OoI OoII 0.5 OoInt NGC 2210 0.45 NGC 1466 Reticulum NGC 1786 0.4 -2.4 -2.2 -2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 [Fe/H]
Figure 10.10: The average V -band absolute magnitude, hMV i, for RRab stars vs cluster metallicity.
135 Chapter 11: Conclusions
The data sets obtained for this dissertation are the best BV photometric data sets yet obtained for the target clusters. The size and quality of the data sets allowed for the identification of new variable stars; for previously known variable stars, the data sets yielded better sampled light curves than had been obtained previously. These more complete light curves allowed for the identification of double modes in several RR Lyrae stars that had previously been considered to be single mode pulsators. Traditionally the number fraction of RRc stars compared to the total number of RR Lyrae stars in a cluster has been used to compare clusters and to serve as an indicator of Oosterhoff status. Since all four of the clusters that were examined turned out to have RRd stars that had been previously misidentified as single mode RR Lyrae stars, mostly RRc stars, it is likely that similarly misidentified RRd stars exist in a large fraction of previously studied globular clusters. Because of this, the number fraction of RRc stars should be changed to the number fraction of first overtone dominant pulsators, RRc and RRd stars. This allows for more accurate comparisons to be made with clusters that have been less well studied, and thus likely have RRd stars included with their RRc stars. The ability of various properties of the RR Lyrae populations in stellar systems to serve as indicators of Oosterhoff status was examined. The average period of RRab stars provides the definition for the Oosterhoff classes and the correlation between hPabi and other properties was checked. The minimum period of RRab stars in a
136 cluster, Pab,min showed a strong correlation with hPabi and little overlap in values between Oo-I and Oo-II clusters, making it a good indicator of Oosterhoff status. Oo- int clusters fell along the same trend in hPabi vs Pab,min as Oo-I and Oo-II clusters, forming a smooth transition between the other two Oosterhoff types. The average RRc period showed a general correlation with the average RRab period but the overlap in values between different Oo-I and Oo-II clusters makes hPci not as strong of an indicator of Oosterhoff status. The other two values examined, the number fraction of RRc stars and the maximum period of the RRc stars in a clusters, both showed little correlation with hPabi and had a significant amount of overlap in values between the Oosterhoff classes, meaning neither quantity is a useful indicator of Oosterhoff type. This is a break from tradition for the number fraction of RRc stars which had previously been used as an indicator of Oosterhoff type. Physical properties, derived from Fourier decomposition of their light curves, were calculated for the first time for the RR Lyrae stars in the target clusters. This is also the first time that physical properties have been calculated for RR Lyrae stars in extragalactic stellar systems. The physical properties were plotted as a function of cluster metallicity and the results for the clusters in this study were compared against those for previously studied Milky Way globular clusters. Mass, effective tempera- ture, and luminosity of RRc stars and the effective temperature of RRab stars all displayed linear trends when looked at as a function of cluster metallicity. The LMC clusters obeyed the same trends as the Milky Way clusters and all three Oosterhoff types followed the same trends, suggesting that the physical processes involved in the formation of the RR Lyrae stars is the same in Galactic and extragalactic clusters and for all Oosterhoff types.
The absolute V magnitude, MV , was the one physical property that did not show a linear trend as a function of cluster metallicity, appearing instead as a step function with Oo-I clusters being fainter than Oo-II clusters. The Oo-int clusters fall on both
137 sides of the step function, with NGC 1466 and the previously studied Milky Way globular cluster lieing with the Oo-I clusters while NGC 2210 fell with the Oo-II clusters. The behavior of the RRab stars on the Bailey diagram proved to be more com- plicated for Oo-int clusters than what is seen in Oo-I and Oo-II clusters. The RR Lyrae stars in Oo-I and Oo-II clusters tend to fall around loci on the Bailey dia- gram. An examination of the Bailey diagrams for NGC 1466 and NGC 2210, as well as the previously studied globular cluster NGC 2257 and dwarf galaxies CVn-I and Draco, reveals that no such locus exists for Oo-int clusters; instead these clusters show a wide range of Bailey diagram behavior. NGC 1466 and Draco have RRab stars that fall near the Oo-I locus while NGC 2210 and NGC 2257 fall near the Oo-II locus. Horizontal branch type seems to be connected to this difference between Oo-int clusters. The Bailey diagram of NGC 1466 was compared against that of Milky Way glob- ular cluster M3, an Oo-I cluster. The same was done with NGC 2210 and M15, a Milky Way Oo-II globular cluster. The RRab stars in NGC 1466 and NGC 2210 showed similar behavior to the RRab stars in their comparison clusters, though with more scatter in the case of NGC 1466. The difference in Pab,min, which represents the transition period between RRab and RRc, between NGC 1466/NGC2210 and the clusters they were compared to, seems to be a factor in why these clusters where classified as Oo-int instead of Oo-I/Oo-II. The RRd stars in the examined clusters showed behavior that was not necessarily related to the behavior of the RRab stars. While the RRd stars in Reticulum and NGC 1466 fell into the region of the Petersen diagram that is occuppied by Milky Way Oo-I globular clusters, consistent with the Bailey diagram behavior of their RRab stars, the RRd stars in NGC 2257 and Draco show behavior that is opposite of their RRab stars. There is some indication however that the behavior of the RRd
138 stars follows the behavior of the RRc stars in the clusters, which is logical as they are all first overtone dominant pulsators. The results presented in this dissertation concerning the behavior of the RRab and RRd stars and the absolute magnitude of the RRab stars in Oo-int objects show that Oosterhoff intermediate objects do not represent a separate, homogenous class. Instead the Oo-int objects seem to be a sort of transition between Oo-I and Oo-II objects. This dissertation significantly increased the sample size of Oo-int objects that have been studied to this level of detail; only M75, NGC 2257, and the Draco dwarf galaxy had previously been studied at close to this level of detail. The sample size of well studied Oo-int objects remains small though and additional Oo-int objects need to be looked at in order for this class and the Oosterhoff phenomenon to be fully understood. The RRab stars in CVn-I seem to display a middle-ground between the behavior of the RRab stars in the other Oo-int clusters. This makes CVn-I, and other Oo-int objects that may be similar to it, a target of particular interest for future study.
139 APPENDICES
140 Appendix A: NGC 1466 Light Curves
Figure A.1: Light curves for the variable stars in NGC 1466
141 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
0.6 P_0 V 18.8 0.4 19 0.2 19.2 0 19.4 -0.2 19.6 -0.4 19.8 0.6 P_1 B 19.2 0.4 19.4 0.2 19.6 0 19.8 -0.2 20 -0.4 20.2
0 0.5 1 1.5 2 0 0.5 1 1.5 2 Phase Phase
142 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
0.6 P_0 V 18.8 0.4 19 0.2 19.2 0 19.4 -0.2 19.6 -0.4 19.8 0.6 P_1 B 19.2 0.4 19.4 0.2 19.6 0 19.8 -0.2 20 -0.4 20.2
0 0.5 1 1.5 2 0 0.5 1 1.5 2 Phase Phase
143 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
144 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
145 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
0.6 P_0 V 18.8 0.4 19 0.2 19.2 0 19.4 -0.2 19.6 -0.4 19.8 0.6 P_1 B 19.2 0.4 19.4 0.2 19.6 0 19.8 -0.2 20 -0.4 20.2
0 0.5 1 1.5 2 0 0.5 1 1.5 2 Phase Phase
146 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
147 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
0.6 P_0 V 18.8 0.4 19 0.2 19.2 0 19.4 -0.2 19.6 -0.4 19.8 0.6 P_1 B 19.2 0.4 19.4 0.2 19.6 0 19.8 -0.2 20 -0.4 20.2
0 0.5 1 1.5 2 0 0.5 1 1.5 2 Phase Phase
148 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
149 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
150 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
151 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
152 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
153 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
154 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
0.6 P_0 V 18.8 0.4 19 0.2 19.2 0 19.4 -0.2 19.6 -0.4 19.8 0.6 P_1 B 19.2 0.4 19.4 0.2 19.6 0 19.8 -0.2 20 -0.4 20.2
0 0.5 1 1.5 2 0 0.5 1 1.5 2 Phase Phase
155 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
0.6 P_0 V 18.8 0.4 19 0.2 19.2 0 19.4 -0.2 19.6 -0.4 19.8 0.6 P_1 B 19.2 0.4 19.4 0.2 19.6 0 19.8 -0.2 20 -0.4 20.2
0 0.5 1 1.5 2 0 0.5 1 1.5 2 Phase Phase
156 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
157 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
0.6 P_0 V 18.8 0.4 19 0.2 19.2 0 19.4 -0.2 19.6 -0.4 19.8 0.6 P_1 B 19.2 0.4 19.4 0.2 19.6 0 19.8 -0.2 20 -0.4 20.2
0 0.5 1 1.5 2 0 0.5 1 1.5 2 Phase Phase
158 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
159 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
160 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
161 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
162 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
163 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
164 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
165 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
0.6 P_0 V 18.8 0.4 19 0.2 19.2 0 19.4 -0.2 19.6 -0.4 19.8 0.6 P_1 B 19.2 0.4 19.4 0.2 19.6 0 19.8 -0.2 20 -0.4 20.2
0 0.5 1 1.5 2 0 0.5 1 1.5 2 Phase Phase
166 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
167 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
168 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
169 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
170 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
171 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
172 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
173 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
174 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
175 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
176 Figure A.1: Light curves for the variable stars in NGC 1466 (continued)
177 Appendix B: Reticulum Light Curves
Figure B.1: Light curves for the variable stars in Reticulum
178 Figure B.1: Light curves for the variable stars in Reticulum (continued)
179 Figure B.1: Light curves for the variable stars in Reticulum (continued)
0.6 P_0 V 18.4 0.4 18.6 0.2 18.8 0 19 -0.2 19.2 -0.4 19.4 0.6 P_1 B 18.8 0.4 19 0.2 19.2 0 19.4 -0.2 19.6 -0.4 19.8
0 0.5 1 1.5 2 0 0.5 1 1.5 2 Phase Phase
180 Figure B.1: Light curves for the variable stars in Reticulum (continued)
0.6 P_0 V 18.4 0.4 18.6 0.2 18.8 0 19 -0.2 19.2 -0.4 19.4 0.6 P_1 B 18.8 0.4 19 0.2 19.2 0 19.4 -0.2 19.6 -0.4 19.8
0 0.5 1 1.5 2 0 0.5 1 1.5 2 Phase Phase
181 Figure B.1: Light curves for the variable stars in Reticulum (continued)
182 Figure B.1: Light curves for the variable stars in Reticulum (continued)
183 Figure B.1: Light curves for the variable stars in Reticulum (continued)
184 Figure B.1: Light curves for the variable stars in Reticulum (continued)
185 Figure B.1: Light curves for the variable stars in Reticulum (continued)
186 Figure B.1: Light curves for the variable stars in Reticulum (continued)
0.6 P_0 V 18.4 0.4 18.6 0.2 18.8 0 19 -0.2 19.2 -0.4 19.4 0.6 P_1 B 18.8 0.4 19 0.2 19.2 0 19.4 -0.2 19.6 -0.4 19.8
0 0.5 1 1.5 2 0 0.5 1 1.5 2 Phase Phase
187 Figure B.1: Light curves for the variable stars in Reticulum (continued)
188 Figure B.1: Light curves for the variable stars in Reticulum (continued)
189 Figure B.1: Light curves for the variable stars in Reticulum (continued)
190 Figure B.1: Light curves for the variable stars in Reticulum (continued)
191 Figure B.1: Light curves for the variable stars in Reticulum (continued)
0.6 P_0 V 18.4 0.4 18.6 0.2 18.8 0 19 -0.2 19.2 -0.4 19.4 0.6 P_1 B 18.8 0.4 19 0.2 19.2 0 19.4 -0.2 19.6 -0.4 19.8
0 0.5 1 1.5 2 0 0.5 1 1.5 2 Phase Phase
192 Figure B.1: Light curves for the variable stars in Reticulum (continued)
193 Figure B.1: Light curves for the variable stars in Reticulum (continued)
194 Figure B.1: Light curves for the variable stars in Reticulum (continued)
195 Figure B.1: Light curves for the variable stars in Reticulum (continued)
196 Figure B.1: Light curves for the variable stars in Reticulum (continued)
0.6 P_0 V 18.4 0.4 18.6 0.2 18.8 0 19 -0.2 19.2 -0.4 19.4 0.6 P_1 B 18.8 0.4 19 0.2 19.2 0 19.4 -0.2 19.6 -0.4 19.8
0 0.5 1 1.5 2 0 0.5 1 1.5 2 Phase Phase
197 Appendix C: NGC 1786 Light Curves
Figure C.1: Light curves for the variable stars in NGC 1786
198 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
0.6 18.5 P_0 V 0.4
0.2 19
0
-0.2 19.5 -0.4
0.6 P_1 B 0.4 19
0.2
0 19.5 -0.2
-0.4 20
0 0.5 1 1.5 2 0 0.5 1 1.5 2 Phase Phase
199 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
200 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
201 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
202 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
203 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
204 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
205 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
206 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
207 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
208 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
0.6 P_0 V 0.4 19
0.2
0 19.5
-0.2
-0.4 20
0.6 P_1 B 0.4
0.2 19.5
0
-0.2 20
-0.4
0 0.5 1 1.5 2 0 0.5 1 1.5 2 Phase Phase
209 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
210 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
211 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
212 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
0.6 18.5 P_0 V 0.4
0.2 19
0
-0.2 19.5
-0.4
0.6 P_1 B 0.4 19
0.2
0 19.5 -0.2
-0.4 20
0 0.5 1 1.5 2 0 0.5 1 1.5 2 Phase Phase
213 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
214 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
215 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
216 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
217 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
218 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
219 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
220 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
221 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
222 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
223 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
0.6 18.5 P_0 V 0.4
0.2 19
0
-0.2 19.5
-0.4
0.6 P_1 B 19 0.4
0.2
19.5 0
-0.2
-0.4 20
0 0.5 1 1.5 2 0 0.5 1 1.5 2 Phase Phase
224 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
225 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
226 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
227 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
228 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
229 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
230 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
231 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
232 Figure C.1: Light curves for the variable stars in NGC 1786 (continued)
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